LMFDB - Embedded newform 210.2.x.a.23.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.15
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.46494 - 0.924094i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.480420 - 2.18385i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.29210 - 2.70749i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.46494 - 0.924094i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.480420 - 2.18385i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.29210 - 2.70749i) q^{9} +(-1.02927 - 1.98509i) q^{10} +(-5.16739 + 2.98339i) q^{11} +(0.806628 - 1.53276i) q^{12} +(2.36809 + 2.36809i) q^{13} +(-0.330568 + 2.62502i) q^{14} +(-2.72187 - 2.75525i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.245156 - 0.914934i) q^{17} +(0.547324 - 2.94965i) q^{18} +(4.22990 + 2.44213i) q^{19} +(-1.50798 - 1.65106i) q^{20} +(0.800996 + 4.51203i) q^{21} +(-4.21916 + 4.21916i) q^{22} +(-0.0558604 - 0.208474i) q^{23} +(0.382436 - 1.68930i) q^{24} +(-4.53839 + 2.09833i) q^{25} +(2.90030 + 1.67449i) q^{26} +(-0.609122 - 5.16033i) q^{27} +(0.360100 + 2.62113i) q^{28} +2.38403 q^{29} +(-3.34224 - 1.95690i) q^{30} +(1.28677 + 2.22875i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.81298 + 9.14565i) q^{33} -0.947209i q^{34} +(5.83027 + 1.00399i) q^{35} +(-0.234751 - 2.99080i) q^{36} +(-0.352701 - 1.31630i) q^{37} +(4.71784 + 1.26414i) q^{38} +(5.65744 + 1.28077i) q^{39} +(-1.88392 - 1.20451i) q^{40} -4.15479i q^{41} +(1.94150 + 4.15097i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(-2.98339 + 5.16739i) q^{44} +(-6.53349 - 1.52102i) q^{45} +(-0.107914 - 0.186912i) q^{46} +(-3.61867 + 0.969620i) q^{47} +(-0.0678189 - 1.73072i) q^{48} +(-5.00516 - 4.89371i) q^{49} +(-3.84066 + 3.20145i) q^{50} +(-0.486346 - 1.56687i) q^{51} +(3.23487 + 0.866780i) q^{52} +(-5.98451 - 1.60355i) q^{53} +(-1.92396 - 4.82684i) q^{54} +(8.99780 + 9.85151i) q^{55} +(1.02623 + 2.43862i) q^{56} +(8.45331 - 0.331246i) q^{57} +(2.30280 - 0.617033i) q^{58} +(2.02618 + 3.50944i) q^{59} +(-3.73484 - 1.02519i) q^{60} +(-6.70029 + 11.6052i) q^{61} +(1.81977 + 1.81977i) q^{62} +(5.34295 + 5.86966i) q^{63} -1.00000i q^{64} +(4.03387 - 6.30922i) q^{65} +(-2.28191 + 10.0797i) q^{66} +(-9.28310 - 2.48740i) q^{67} +(-0.245156 - 0.914934i) q^{68} +(-0.274482 - 0.253781i) q^{69} +(5.89146 - 0.539201i) q^{70} +10.7537i q^{71} +(-1.00083 - 2.82813i) q^{72} +(3.43327 - 12.8131i) q^{73} +(-0.681365 - 1.18016i) q^{74} +(-4.70942 + 7.26783i) q^{75} +4.88427 q^{76} +(-2.14864 - 15.6397i) q^{77} +(5.79616 - 0.227124i) q^{78} +(0.874016 + 0.504613i) q^{79} +(-2.13148 - 0.675868i) q^{80} +(-5.66096 - 6.99668i) q^{81} +(-1.07534 - 4.01322i) q^{82} +(7.84434 - 7.84434i) q^{83} +(2.94970 + 3.50703i) q^{84} +(-2.11586 - 0.0958303i) q^{85} +(-7.37384 - 4.25729i) q^{86} +(3.49247 - 2.20307i) q^{87} +(-1.54432 + 5.76347i) q^{88} +(0.188917 - 0.327214i) q^{89} +(-6.70454 + 0.221800i) q^{90} +(-8.16688 + 3.43682i) q^{91} +(-0.152613 - 0.152613i) q^{92} +(3.94461 + 2.07589i) q^{93} +(-3.24441 + 1.87316i) q^{94} +(3.30112 - 10.4107i) q^{95} +(-0.513452 - 1.65420i) q^{96} +(3.42689 - 3.42689i) q^{97} +(-6.10120 - 3.43153i) q^{98} +(1.40071 + 17.8455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.46494	−	0.924094i	0.845784	−	0.533526i
$3$	1.46494	−	0.924094i	0.845784	−	0.533526i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.480420	−	2.18385i	−0.214851	−	0.976647i
$5$	−0.480420	−	2.18385i	−0.214851	−	0.976647i
$6$	1.17585	−	1.27176i	0.480039	−	0.519194i
$7$	−0.998710	+	2.45002i	−0.377477	+	0.926019i
$7$	−0.998710	+	2.45002i	−0.377477	+	0.926019i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.29210	−	2.70749i	0.430700	−	0.902495i
$10$	−1.02927	−	1.98509i	−0.325484	−	0.627742i
$11$	−5.16739	+	2.98339i	−1.55803	+	0.899527i	−0.560581	+	0.828100i	$0.689422\pi$
$11$	−5.16739	+	2.98339i	−1.55803	+	0.899527i	−0.997446	+	0.0714273i	$0.977245\pi$
$12$	0.806628	−	1.53276i	0.232854	−	0.442469i
$13$	2.36809	+	2.36809i	0.656789	+	0.656789i	0.954619	−	0.297830i	$-0.0962628\pi$
$13$	2.36809	+	2.36809i	0.656789	+	0.656789i	−0.297830	+	0.954619i	$0.596263\pi$
$14$	−0.330568	+	2.62502i	−0.0883481	+	0.701566i
$15$	−2.72187	−	2.75525i	−0.702784	−	0.711404i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.245156	−	0.914934i	0.0594590	−	0.221904i	−0.929803	−	0.368058i	$-0.880023\pi$
$17$	0.245156	−	0.914934i	0.0594590	−	0.221904i	0.989262	+	0.146154i	$0.0466895\pi$
$18$	0.547324	−	2.94965i	0.129005	−	0.695239i
$19$	4.22990	+	2.44213i	0.970406	+	0.560264i	0.899360	−	0.437209i	$-0.144033\pi$
$19$	4.22990	+	2.44213i	0.970406	+	0.560264i	0.0710458	+	0.997473i	$0.477366\pi$
$20$	−1.50798	−	1.65106i	−0.337195	−	0.369188i
$21$	0.800996	+	4.51203i	0.174792	+	0.984605i
$22$	−4.21916	+	4.21916i	−0.899527	+	0.899527i
$23$	−0.0558604	−	0.208474i	−0.0116477	−	0.0434698i	0.959857	−	0.280488i	$-0.0904964\pi$
$23$	−0.0558604	−	0.208474i	−0.0116477	−	0.0434698i	−0.971505	+	0.237019i	$0.923830\pi$
$24$	0.382436	−	1.68930i	0.0780644	−	0.344827i
$25$	−4.53839	+	2.09833i	−0.907678	+	0.419666i
$26$	2.90030	+	1.67449i	0.568796	+	0.328395i
$27$	−0.609122	−	5.16033i	−0.117226	−	0.993105i
$28$	0.360100	+	2.62113i	0.0680526	+	0.495347i
$29$	2.38403			0.442704			0.221352	−	0.975194i	$-0.428953\pi$
$29$	2.38403			0.442704			0.221352	+	0.975194i	$0.428953\pi$
$30$	−3.34224	−	1.95690i	−0.610206	−	0.357279i
$31$	1.28677	+	2.22875i	0.231110	+	0.400295i	0.958135	−	0.286316i	$-0.0924308\pi$
$31$	1.28677	+	2.22875i	0.231110	+	0.400295i	−0.727025	+	0.686611i	$0.759097\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−4.81298	+	9.14565i	−0.837832	+	1.59205i
$34$		−	0.947209i		−	0.162445i
$35$	5.83027	+	1.00399i	0.985495	+	0.169706i
$36$	−0.234751	−	2.99080i	−0.0391252	−	0.498467i
$37$	−0.352701	−	1.31630i	−0.0579836	−	0.216398i	0.930855	−	0.365389i	$-0.119064\pi$
$37$	−0.352701	−	1.31630i	−0.0579836	−	0.216398i	−0.988839	+	0.148991i	$0.952397\pi$
$38$	4.71784	+	1.26414i	0.765335	+	0.205071i
$39$	5.65744	+	1.28077i	0.905916	+	0.205087i
$40$	−1.88392	−	1.20451i	−0.297874	−	0.190449i
$41$		−	4.15479i		−	0.648869i	−0.945908	−	0.324435i	$-0.894826\pi$
$41$		−	4.15479i		−	0.648869i	0.945908	−	0.324435i	$-0.105174\pi$
$42$	1.94150	+	4.15097i	0.299580	+	0.640509i
$43$	−6.02072	−	6.02072i	−0.918151	−	0.918151i	0.0787443	−	0.996895i	$-0.474909\pi$
$43$	−6.02072	−	6.02072i	−0.918151	−	0.918151i	−0.996895	+	0.0787443i	$0.974909\pi$
$44$	−2.98339	+	5.16739i	−0.449764	+	0.779013i
$45$	−6.53349	−	1.52102i	−0.973955	−	0.226740i
$46$	−0.107914	−	0.186912i	−0.0159110	−	0.0275587i
$47$	−3.61867	+	0.969620i	−0.527838	+	0.141434i	−0.512890	−	0.858455i	$-0.671425\pi$
$47$	−3.61867	+	0.969620i	−0.527838	+	0.141434i	−0.0149481	+	0.999888i	$0.504758\pi$
$48$	−0.0678189	−	1.73072i	−0.00978882	−	0.249808i
$49$	−5.00516	−	4.89371i	−0.715023	−	0.699101i
$50$	−3.84066	+	3.20145i	−0.543152	+	0.452754i
$51$	−0.486346	−	1.56687i	−0.0681021	−	0.219406i
$52$	3.23487	+	0.866780i	0.448595	+	0.120201i
$53$	−5.98451	−	1.60355i	−0.822036	−	0.220264i	−0.176800	−	0.984247i	$-0.556574\pi$
$53$	−5.98451	−	1.60355i	−0.822036	−	0.220264i	−0.645236	+	0.763983i	$0.723241\pi$
$54$	−1.92396	−	4.82684i	−0.261818	−	0.656850i
$55$	8.99780	+	9.85151i	1.21326	+	1.32838i
$56$	1.02623	+	2.43862i	0.137136	+	0.325874i
$57$	8.45331	−	0.331246i	1.11967	−	0.0438746i
$58$	2.30280	−	0.617033i	0.302372	−	0.0810204i
$59$	2.02618	+	3.50944i	0.263786	+	0.456890i	0.967245	−	0.253846i	$-0.0816955\pi$
$59$	2.02618	+	3.50944i	0.263786	+	0.456890i	−0.703459	+	0.710736i	$0.748362\pi$
$60$	−3.73484	−	1.02519i	−0.482165	−	0.132351i
$61$	−6.70029	+	11.6052i	−0.857884	+	1.48590i	0.0160589	+	0.999871i	$0.494888\pi$
$61$	−6.70029	+	11.6052i	−0.857884	+	1.48590i	−0.873943	+	0.486028i	$0.838445\pi$
$62$	1.81977	+	1.81977i	0.231110	+	0.231110i
$63$	5.34295	+	5.86966i	0.673149	+	0.739507i
$64$		−	1.00000i		−	0.125000i
$65$	4.03387	−	6.30922i	0.500340	−	0.782563i
$66$	−2.28191	+	10.0797i	−0.280884	+	1.24073i
$67$	−9.28310	−	2.48740i	−1.13411	−	0.303884i	−0.357530	−	0.933902i	$-0.616381\pi$
$67$	−9.28310	−	2.48740i	−1.13411	−	0.303884i	−0.776581	+	0.630017i	$0.783048\pi$
$68$	−0.245156	−	0.914934i	−0.0297295	−	0.110952i
$69$	−0.274482	−	0.253781i	−0.0330437	−	0.0305517i
$70$	5.89146	−	0.539201i	0.704164	−	0.0644469i
$71$			10.7537i			1.27623i	0.769943	+	0.638113i	$0.220285\pi$
$71$			10.7537i			1.27623i	−0.769943	+	0.638113i	$0.779715\pi$
$72$	−1.00083	−	2.82813i	−0.117949	−	0.333299i
$73$	3.43327	−	12.8131i	0.401834	−	1.49967i	−0.407987	−	0.912988i	$-0.633769\pi$
$73$	3.43327	−	12.8131i	0.401834	−	1.49967i	0.809821	−	0.586677i	$-0.199564\pi$
$74$	−0.681365	−	1.18016i	−0.0792071	−	0.137191i
$75$	−4.70942	+	7.26783i	−0.543797	+	0.839217i
$76$	4.88427			0.560264
$77$	−2.14864	−	15.6397i	−0.244860	−	1.78231i
$78$	5.79616	−	0.227124i	0.656286	−	0.0257168i
$79$	0.874016	+	0.504613i	0.0983345	+	0.0567734i	0.548361	−	0.836242i	$-0.315252\pi$
$79$	0.874016	+	0.504613i	0.0983345	+	0.0567734i	−0.450026	+	0.893015i	$0.648585\pi$
$80$	−2.13148	−	0.675868i	−0.238307	−	0.0755644i
$81$	−5.66096	−	6.99668i	−0.628995	−	0.777409i
$82$	−1.07534	−	4.01322i	−0.118751	−	0.443186i
$83$	7.84434	−	7.84434i	0.861028	−	0.861028i	−0.130429	−	0.991458i	$-0.541636\pi$
$83$	7.84434	−	7.84434i	0.861028	−	0.861028i	0.991458	+	0.130429i	$0.0416356\pi$
$84$	2.94970	+	3.50703i	0.321838	+	0.382649i
$85$	−2.11586	−	0.0958303i	−0.229497	−	0.0103943i
$86$	−7.37384	−	4.25729i	−0.795142	−	0.459075i
$87$	3.49247	−	2.20307i	0.374432	−	0.236194i
$88$	−1.54432	+	5.76347i	−0.164625	+	0.614388i
$89$	0.188917	−	0.327214i	0.0200252	−	0.0346846i	−0.855839	−	0.517242i	$-0.826959\pi$
$89$	0.188917	−	0.327214i	0.0200252	−	0.0346846i	0.875864	+	0.482557i	$0.160292\pi$
$90$	−6.70454	+	0.221800i	−0.706720	+	0.0233797i
$91$	−8.16688	+	3.43682i	−0.856122	+	0.360277i
$92$	−0.152613	−	0.152613i	−0.0159110	−	0.0159110i
$93$	3.94461	+	2.07589i	0.409037	+	0.215260i
$94$	−3.24441	+	1.87316i	−0.334636	+	0.193202i
$95$	3.30112	−	10.4107i	0.338688	−	1.06812i
$96$	−0.513452	−	1.65420i	−0.0524040	−	0.168831i
$97$	3.42689	−	3.42689i	0.347948	−	0.347948i	−0.511397	−	0.859345i	$-0.670872\pi$
$97$	3.42689	−	3.42689i	0.347948	−	0.347948i	0.859345	+	0.511397i	$0.170872\pi$
$98$	−6.10120	−	3.43153i	−0.616314	−	0.346637i
$99$	1.40071	+	17.8455i	0.140777	+	1.79354i
$100$	−2.88120	+	4.08640i	−0.288120	+	0.408640i
$101$	3.73396	−	2.15580i	0.371543	−	0.214510i	−0.302589	−	0.953121i	$-0.597851\pi$
$101$	3.73396	−	2.15580i	0.371543	−	0.214510i	0.674132	+	0.738611i	$0.264518\pi$
$102$	−0.875311	−	1.38760i	−0.0866687	−	0.137393i
$103$	12.9118	−	3.45971i	1.27224	−	0.340896i	0.441352	−	0.897334i	$-0.354499\pi$
$103$	12.9118	−	3.45971i	1.27224	−	0.340896i	0.830889	+	0.556438i	$0.187833\pi$
$104$	3.34898			0.328395
$105$	9.46877	−	3.91692i	0.924058	−	0.382253i
$106$	−6.19562			−0.601772
$107$	−15.2003	+	4.07291i	−1.46947	+	0.393743i	−0.902749	−	0.430168i	$-0.858454\pi$
$107$	−15.2003	+	4.07291i	−1.46947	+	0.393743i	−0.566720	+	0.823911i	$0.691788\pi$
$108$	−3.10768	−	4.16441i	−0.299037	−	0.400721i
$109$	9.16343	−	5.29051i	0.877698	−	0.506739i	0.00779912	−	0.999970i	$-0.497517\pi$
$109$	9.16343	−	5.29051i	0.877698	−	0.506739i	0.869899	+	0.493231i	$0.164184\pi$
$110$	11.2410	+	7.18703i	1.07178	+	0.685256i
$111$	−1.73307	−	1.60237i	−0.164495	−	0.152090i
$112$	1.62242	+	2.08992i	0.153304	+	0.197478i
$113$	5.87797	−	5.87797i	0.552953	−	0.552953i	−0.374339	−	0.927292i	$-0.622130\pi$
$113$	5.87797	−	5.87797i	0.552953	−	0.552953i	0.927292	+	0.374339i	$0.122130\pi$
$114$	8.07954	−	2.50784i	0.756718	−	0.234880i
$115$	−0.428439	+	0.222146i	−0.0399521	+	0.0207152i
$116$	2.06463	−	1.19202i	0.191696	−	0.110676i
$117$	9.47137	−	3.35176i	0.875628	−	0.309870i
$118$	2.86545	+	2.86545i	0.263786	+	0.263786i
$119$	1.99676	+	1.51439i	0.183043	+	0.138824i
$120$	−3.87291	−	0.0236070i	−0.353547	−	0.00215501i
$121$	12.3013	−	21.3064i	1.11830	−	1.93695i
$122$	−3.46833	+	12.9440i	−0.314007	+	1.17189i
$123$	−3.83942	−	6.08652i	−0.346189	−	0.548803i
$124$	2.22875	+	1.28677i	0.200147	+	0.115555i
$125$	6.76277	+	8.90308i	0.604881	+	0.796316i
$126$	6.68007	+	4.28680i	0.595108	+	0.381898i
$127$	11.0815	−	11.0815i	0.983320	−	0.983320i	−0.0165433	−	0.999863i	$-0.505266\pi$
$127$	11.0815	−	11.0815i	0.983320	−	0.983320i	0.999863	+	0.0165433i	$0.00526612\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−14.3837	−	3.25628i	−1.26641	−	0.286699i
$130$	2.26347	−	7.13828i	0.198519	−	0.626069i
$131$	3.73610	+	2.15704i	0.326424	+	0.188461i	0.654252	−	0.756276i	$-0.272983\pi$
$131$	3.73610	+	2.15704i	0.326424	+	0.188461i	−0.327828	+	0.944737i	$0.606317\pi$
$132$	0.404661	+	10.3269i	0.0352212	+	0.898837i
$133$	−10.2077	+	7.92434i	−0.885121	+	0.687128i
$134$	−9.61057			−0.830227
$135$	−10.9767	+	3.80936i	−0.944727	+	0.327857i
$136$	−0.473605	−	0.820307i	−0.0406113	−	0.0703408i
$137$	−2.10404	+	7.85237i	−0.179760	+	0.670874i	0.815932	+	0.578148i	$0.196225\pi$
$137$	−2.10404	+	7.85237i	−0.179760	+	0.670874i	−0.995692	+	0.0927253i	$0.970442\pi$
$138$	−0.330812	−	0.174093i	−0.0281606	−	0.0148198i
$139$		−	10.9242i		−	0.926578i	−0.886207	−	0.463289i	$-0.846669\pi$
$139$		−	10.9242i		−	0.926578i	0.886207	−	0.463289i	$-0.153331\pi$
$140$	5.55115	−	2.04565i	0.469158	−	0.172889i
$141$	−4.40512	+	4.76443i	−0.370978	+	0.401237i
$142$	2.78326	+	10.3873i	0.233566	+	0.871679i
$143$	−19.3018	−	5.17189i	−1.61409	−	0.432495i
$144$	−1.69870	−	2.47273i	−0.141558	−	0.206061i
$145$	−1.14534	−	5.20637i	−0.0951152	−	0.432365i
$146$		−	13.2651i		−	1.09783i
$147$	−11.8545	−	2.54375i	−0.977743	−	0.209805i
$148$	−0.963596	−	0.963596i	−0.0792071	−	0.0792071i
$149$	−5.86144	+	10.1523i	−0.480188	+	0.831710i	−0.999742	−	0.0227275i	$-0.992765\pi$
$149$	−5.86144	+	10.1523i	−0.480188	+	0.831710i	0.519553	+	0.854438i	$0.326098\pi$
$150$	−2.66790	+	8.23907i	−0.217833	+	0.672718i
$151$	8.24246	+	14.2764i	0.670762	+	1.16179i	0.977688	+	0.210060i	$0.0673660\pi$
$151$	8.24246	+	14.2764i	0.670762	+	1.16179i	−0.306927	+	0.951733i	$0.599301\pi$
$152$	4.71784	−	1.26414i	0.382667	−	0.102535i
$153$	−2.16040	−	1.84594i	−0.174658	−	0.149236i
$154$	−6.12329	−	14.5507i	−0.493429	−	1.17253i
$155$	4.24906	−	3.88084i	0.341293	−	0.311717i
$156$	5.53987	−	1.71954i	0.443545	−	0.137673i
$157$	2.43060	+	0.651278i	0.193983	+	0.0519776i	0.354503	−	0.935055i	$-0.384650\pi$
$157$	2.43060	+	0.651278i	0.193983	+	0.0519776i	−0.160519	+	0.987033i	$0.551317\pi$
$158$	0.974838	+	0.261207i	0.0775540	+	0.0207805i
$159$	−10.2488	+	3.18116i	−0.812781	+	0.252282i
$160$	−2.23378	−	0.101171i	−0.176596	−	0.00799829i
$161$	0.566552	+	0.0713459i	0.0446506	+	0.00562285i
$162$	−7.27894	−	5.29311i	−0.571887	−	0.415866i
$163$	−4.86553	+	1.30371i	−0.381097	+	0.102115i	−0.444282	−	0.895887i	$-0.646541\pi$
$163$	−4.86553	+	1.30371i	−0.381097	+	0.102115i	0.0631843	+	0.998002i	$0.479874\pi$
$164$	−2.07740	−	3.59815i	−0.162217	−	0.280969i
$165$	22.2850	+	6.11707i	1.73488	+	0.476213i
$166$	5.54679	−	9.60731i	0.430514	−	0.745672i
$167$	13.6846	+	13.6846i	1.05894	+	1.05894i	0.998150	+	0.0607934i	$0.0193631\pi$
$167$	13.6846	+	13.6846i	1.05894	+	1.05894i	0.0607934	+	0.998150i	$0.480637\pi$
$168$	3.75688	+	2.62410i	0.289849	+	0.202453i
$169$		−	1.78432i		−	0.137256i
$170$	−2.06856	+	0.455059i	−0.158651	+	0.0349014i
$171$	12.0775	−	8.29691i	0.923589	−	0.634481i
$172$	−8.22445	−	2.20373i	−0.627108	−	0.168033i
$173$	−3.67722	−	13.7236i	−0.279574	−	1.04338i	−0.952714	−	0.303869i	$-0.901722\pi$
$173$	−3.67722	−	13.7236i	−0.279574	−	1.04338i	0.673140	−	0.739515i	$-0.264945\pi$
$174$	2.80327	−	3.03192i	0.212515	−	0.229849i
$175$	−0.608409	−	13.2148i	−0.0459914	−	0.998942i
$176$			5.96679i			0.449764i
$177$	6.21128	+	3.26874i	0.466869	+	0.245694i
$178$	0.0977906	−	0.364960i	0.00732972	−	0.0273549i
$179$	4.32841	+	7.49703i	0.323521	+	0.560354i	0.981212	−	0.192934i	$-0.0618002\pi$
$179$	4.32841	+	7.49703i	0.323521	+	0.560354i	−0.657691	+	0.753288i	$0.728467\pi$
$180$	−6.41868	+	1.94950i	−0.478420	+	0.145307i
$181$	−11.7154			−0.870801			−0.435400	−	0.900237i	$-0.643393\pi$
$181$	−11.7154			−0.870801			−0.435400	+	0.900237i	$0.643393\pi$
$182$	−6.99909	+	5.43346i	−0.518807	+	0.402755i
$183$	0.908813	+	23.1927i	0.0671814	+	1.71445i
$184$	−0.186912	−	0.107914i	−0.0137794	−	0.00795552i
$185$	−2.70515	+	1.40262i	−0.198886	+	0.103123i
$186$	4.34748	+	0.984213i	0.318773	+	0.0721660i
$187$	1.46279	+	5.45922i	0.106970	+	0.399217i
$188$	−2.64905	+	2.64905i	−0.193202	+	0.193202i
$189$	13.2512	+	3.66131i	0.963884	+	0.266321i
$190$	0.494147	−	10.9104i	0.0358492	−	0.791522i
$191$	22.6716	+	13.0895i	1.64046	+	0.947120i	0.980670	+	0.195670i	$0.0626883\pi$
$191$	22.6716	+	13.0895i	1.64046	+	0.947120i	0.659790	+	0.751450i	$0.270645\pi$
$192$	−0.924094	−	1.46494i	−0.0666908	−	0.105723i
$193$	−5.50843	+	20.5578i	−0.396506	+	1.47978i	0.422694	+	0.906272i	$0.361084\pi$
$193$	−5.50843	+	20.5578i	−0.396506	+	1.47978i	−0.819200	+	0.573508i	$0.805582\pi$
$194$	2.42318	−	4.19707i	0.173974	−	0.301332i
$195$	0.0790593	−	12.9703i	0.00566155	−	0.928823i
$196$	−6.78145	−	1.73550i	−0.484389	−	0.123964i
$197$	−8.39658	−	8.39658i	−0.598231	−	0.598231i	0.341610	−	0.939842i	$-0.389028\pi$
$197$	−8.39658	−	8.39658i	−0.598231	−	0.598231i	−0.939842	+	0.341610i	$0.889028\pi$
$198$	5.97173	+	16.8749i	0.424393	+	1.19925i
$199$	−16.5482	+	9.55411i	−1.17307	+	0.677273i	−0.954401	−	0.298527i	$-0.903505\pi$
$199$	−16.5482	+	9.55411i	−1.17307	+	0.677273i	−0.218669	+	0.975799i	$0.570172\pi$
$200$	−1.72538	+	4.69287i	−0.122003	+	0.331836i
$201$	−15.8978	+	4.93457i	−1.12134	+	0.348058i
$202$	3.04877	−	3.04877i	0.214510	−	0.214510i
$203$	−2.38096	+	5.84092i	−0.167110	+	0.409952i
$204$	−1.20462	−	1.11378i	−0.0843405	−	0.0779799i
$205$	−9.07344	+	1.99605i	−0.633716	+	0.139410i
$206$	11.5764	−	6.68365i	0.806568	−	0.465672i
$207$	−0.636617	−	0.118128i	−0.0442479	−	0.00821045i
$208$	3.23487	−	0.866780i	0.224298	−	0.0601004i
$209$	−29.1434			−2.01589
$210$	8.13236	−	6.23416i	0.561186	−	0.430198i
$211$	−6.45261			−0.444216			−0.222108	−	0.975022i	$-0.571294\pi$
$211$	−6.45261			−0.444216			−0.222108	+	0.975022i	$0.571294\pi$
$212$	−5.98451	+	1.60355i	−0.411018	+	0.110132i
$213$	9.93741	+	15.7535i	0.680900	+	1.07941i
$214$	−13.6282	+	7.86826i	−0.931606	+	0.537863i
$215$	−10.2559	+	16.0408i	−0.699444	+	1.09397i
$216$	−4.07962	−	3.21819i	−0.277583	−	0.218970i
$217$	−6.74558	+	0.926731i	−0.457920	+	0.0629106i
$218$	7.48191	−	7.48191i	0.506739	−	0.506739i
$219$	−6.81102	−	21.9432i	−0.460246	−	1.48278i
$220$	12.7181	+	4.03276i	0.857453	+	0.271889i
$221$	2.74719	−	1.58609i	0.184796	−	0.106692i
$222$	−2.08874	−	1.09922i	−0.140187	−	0.0737746i
$223$	−6.54087	−	6.54087i	−0.438009	−	0.438009i	0.453333	−	0.891341i	$-0.350235\pi$
$223$	−6.54087	−	6.54087i	−0.438009	−	0.438009i	−0.891341	+	0.453333i	$0.850235\pi$
$224$	2.10805	+	1.59879i	0.140850	+	0.106824i
$225$	−0.182855	+	14.9989i	−0.0121904	+	0.999926i
$226$	4.15635	−	7.19901i	0.276476	−	0.478871i
$227$	−2.54238	+	9.48829i	−0.168744	+	0.629760i	0.828789	+	0.559561i	$0.189030\pi$
$227$	−2.54238	+	9.48829i	−0.168744	+	0.629760i	−0.997533	+	0.0701991i	$0.977637\pi$
$228$	7.15516	−	4.51352i	0.473862	−	0.298915i
$229$	7.87583	+	4.54711i	0.520449	+	0.300482i	0.737118	−	0.675764i	$-0.236186\pi$
$229$	7.87583	+	4.54711i	0.520449	+	0.300482i	−0.216669	+	0.976245i	$0.569519\pi$
$230$	−0.356345	+	0.325464i	−0.0234967	+	0.0214605i
$231$	−17.6002	−	20.9257i	−1.15801	−	1.37681i
$232$	1.68577	−	1.68577i	0.110676	−	0.110676i
$233$	4.84119	+	18.0676i	0.317157	+	1.18364i	0.921965	+	0.387274i	$0.126583\pi$
$233$	4.84119	+	18.0676i	0.317157	+	1.18364i	−0.604808	+	0.796371i	$0.706750\pi$
$234$	8.28114	−	5.68892i	0.541355	−	0.371896i
$235$	3.85599	+	7.43681i	0.251537	+	0.485124i
$236$	3.50944	+	2.02618i	0.228445	+	0.131893i
$237$	1.74669	−	0.0684447i	0.113460	−	0.00444596i
$238$	2.32068	+	0.945987i	0.150427	+	0.0613192i
$239$	8.87693			0.574201			0.287100	−	0.957900i	$-0.407309\pi$
$239$	8.87693			0.574201			0.287100	+	0.957900i	$0.407309\pi$
$240$	−3.74706	+	0.979581i	−0.241871	+	0.0632317i
$241$	2.06335	+	3.57384i	0.132912	+	0.230211i	0.924798	−	0.380458i	$-0.124234\pi$
$241$	2.06335	+	3.57384i	0.132912	+	0.230211i	−0.791886	+	0.610669i	$0.790900\pi$
$242$	6.36761	−	23.7642i	0.409325	−	1.52762i
$243$	−14.7586	−	5.01847i	−0.946762	−	0.321935i
$244$			13.4006i			0.857884i
$245$	−8.28254	+	13.2815i	−0.529152	+	0.848527i
$246$	−5.28390	−	4.88541i	−0.336889	−	0.311483i
$247$	4.23359	+	15.8000i	0.269377	+	1.00533i
$248$	2.48585	+	0.666080i	0.157851	+	0.0422961i
$249$	4.24258	−	18.7404i	0.268863	−	1.18762i
$250$	8.83663	+	6.84938i	0.558877	+	0.433193i
$251$		−	9.72407i		−	0.613778i	−0.951745	−	0.306889i	$-0.900712\pi$
$251$		−	9.72407i		−	0.613778i	0.951745	−	0.306889i	$-0.0992880\pi$
$252$	7.56196	+	2.41180i	0.476359	+	0.151929i
$253$	0.910612	+	0.910612i	0.0572497	+	0.0572497i
$254$	7.83577	−	13.5720i	0.491660	−	0.851580i
$255$	−3.18816	+	1.81486i	−0.199650	+	0.113651i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.07565	+	1.62796i	−0.378988	+	0.101550i	−0.443284	−	0.896381i	$-0.646187\pi$
$257$	−6.07565	+	1.62796i	−0.378988	+	0.101550i	0.0642955	+	0.997931i	$0.479520\pi$
$258$	−14.7364	+	0.577449i	−0.917446	+	0.0359504i
$259$	3.57719	+	0.450476i	0.222276	+	0.0279912i
$260$	0.338821	−	7.48088i	0.0210128	−	0.463945i
$261$	3.08041	−	6.45474i	0.190673	−	0.399538i
$262$	4.16707	+	1.11656i	0.257443	+	0.0689816i
$263$	−12.5532	−	3.36362i	−0.774064	−	0.207410i	−0.149898	−	0.988701i	$-0.547894\pi$
$263$	−12.5532	−	3.36362i	−0.774064	−	0.207410i	−0.624166	+	0.781292i	$0.714561\pi$
$264$	3.06366	+	9.87024i	0.188555	+	0.607471i
$265$	−0.626819	+	13.8396i	−0.0385052	+	0.850163i
$266$	−7.80892	+	10.2963i	−0.478796	+	0.631305i
$267$	−0.0256243	−	0.653926i	−0.00156818	−	0.0400196i
$268$	−9.28310	+	2.48740i	−0.567056	+	0.151942i
$269$	−5.49814	−	9.52306i	−0.335228	−	0.580631i	0.648301	−	0.761384i	$-0.275480\pi$
$269$	−5.49814	−	9.52306i	−0.335228	−	0.580631i	−0.983529	+	0.180753i	$0.942147\pi$
$270$	−9.61678	+	6.52055i	−0.585259	+	0.396828i
$271$	9.59447	−	16.6181i	0.582823	−	1.00948i	−0.412321	−	0.911039i	$-0.635282\pi$
$271$	9.59447	−	16.6181i	0.582823	−	1.00948i	0.995143	−	0.0984394i	$-0.0313851\pi$
$272$	−0.669778	−	0.669778i	−0.0406113	−	0.0406113i
$273$	−8.78805	+	12.5817i	−0.531877	+	0.761480i
$274$			8.12938i			0.491114i
$275$	17.1915	−	24.3827i	1.03669	−	1.47033i
$276$	−0.364599	−	0.0825404i	−0.0219463	−	0.00496835i
$277$	1.66179	+	0.445276i	0.0998475	+	0.0267540i	0.308397	−	0.951258i	$-0.400208\pi$
$277$	1.66179	+	0.445276i	0.0998475	+	0.0267540i	−0.208549	+	0.978012i	$0.566874\pi$
$278$	−2.82739	−	10.5520i	−0.169575	−	0.632864i
$279$	7.69694	−	0.604141i	0.460804	−	0.0361690i
$280$	4.83255	−	3.41269i	0.288800	−	0.203947i
$281$		−	17.7331i		−	1.05787i	−0.848664	−	0.528933i	$-0.822592\pi$
$281$		−	17.7331i		−	1.05787i	0.848664	−	0.528933i	$-0.177408\pi$
$282$	−3.02189	+	5.74221i	−0.179951	+	0.341944i
$283$	4.30819	−	16.0784i	0.256095	−	0.955760i	−0.711383	−	0.702805i	$-0.751931\pi$
$283$	4.30819	−	16.0784i	0.256095	−	0.955760i	0.967478	−	0.252955i	$-0.0814025\pi$
$284$	5.37684	+	9.31295i	0.319057	+	0.552622i
$285$	−4.78453	−	18.3016i	−0.283411	−	1.08409i
$286$	−19.9827			−1.18160
$287$	10.1793	+	4.14943i	0.600865	+	0.244933i
$288$	−2.28081	−	1.94882i	−0.134398	−	0.114835i
$289$	13.9454	+	8.05140i	0.820319	+	0.473612i
$290$	−2.45382	−	4.73253i	−0.144093	−	0.277904i
$291$	1.85342	−	8.18696i	0.108649	−	0.479928i
$292$	−3.43327	−	12.8131i	−0.200917	−	0.749833i
$293$	−5.73680	+	5.73680i	−0.335148	+	0.335148i	−0.854537	−	0.519390i	$-0.826159\pi$
$293$	−5.73680	+	5.73680i	−0.335148	+	0.335148i	0.519390	+	0.854537i	$0.326159\pi$
$294$	−12.1089	+	0.611095i	−0.706208	+	0.0356398i
$295$	6.69067	−	6.11087i	0.389546	−	0.355789i
$296$	−1.18016	−	0.681365i	−0.0685953	−	0.0396035i
$297$	18.5429	+	24.8482i	1.07597	+	1.44184i
$298$	−3.03411	+	11.3234i	−0.175761	+	0.655949i
$299$	0.361402	−	0.625966i	0.0209004	−	0.0362006i
$300$	−0.444560	+	8.64884i	−0.0256667	+	0.499341i
$301$	20.7638	−	8.73790i	1.19681	−	0.503644i
$302$	11.6566	+	11.6566i	0.670762	+	0.670762i
$303$	3.47786	−	6.60865i	0.199798	−	0.379657i
$304$	4.22990	−	2.44213i	0.242601	−	0.140066i
$305$	28.5631	+	9.05703i	1.63552	+	0.518604i
$306$	−2.56456	−	1.22389i	−0.146606	−	0.0699651i
$307$	1.58405	−	1.58405i	0.0904064	−	0.0904064i	−0.660457	−	0.750864i	$-0.729638\pi$
$307$	1.58405	−	1.58405i	0.0904064	−	0.0904064i	0.750864	+	0.660457i	$0.229638\pi$
$308$	−9.68064	−	12.4701i	−0.551606	−	0.710549i
$309$	15.7180	−	17.0000i	0.894163	−	0.967097i
$310$	3.09984	−	4.84834i	0.176059	−	0.275367i
$311$	5.20473	−	3.00495i	0.295133	−	0.170395i	−0.345121	−	0.938558i	$-0.612162\pi$
$311$	5.20473	−	3.00495i	0.295133	−	0.170395i	0.640254	+	0.768163i	$0.278829\pi$
$312$	4.90606	−	3.09477i	0.277751	−	0.175207i
$313$	−3.10488	+	0.831951i	−0.175498	+	0.0470246i	−0.345498	−	0.938419i	$-0.612290\pi$
$313$	−3.10488	+	0.831951i	−0.175498	+	0.0470246i	0.170000	+	0.985444i	$0.445623\pi$
$314$	2.51634			0.142006
$315$	10.2516	−	14.4881i	0.577611	−	0.816312i
$316$	1.00923			0.0567734
$317$	−0.760038	+	0.203652i	−0.0426880	+	0.0114382i	−0.280100	−	0.959971i	$-0.590368\pi$
$317$	−0.760038	+	0.203652i	−0.0426880	+	0.0114382i	0.237412	+	0.971409i	$0.423701\pi$
$318$	−9.07622	+	5.72534i	−0.508969	+	0.321061i
$319$	−12.3192	+	7.11251i	−0.689744	+	0.398224i
$320$	−2.18385	+	0.480420i	−0.122081	+	0.0268563i
$321$	−18.5038	+	20.0131i	−1.03278	+	1.11702i
$322$	0.565713	−	0.0777197i	0.0315260	−	0.00433115i
$323$	3.27138	−	3.27138i	0.182024	−	0.182024i
$324$	−8.40087	−	3.22883i	−0.466715	−	0.179379i
$325$	−15.7163	−	5.77828i	−0.871786	−	0.320521i
$326$	−4.36231	+	2.51858i	−0.241606	+	0.139491i
$327$	8.53495	−	16.2182i	0.471984	−	0.896866i
$328$	−2.93788	−	2.93788i	−0.162217	−	0.162217i
$329$	1.23842	−	9.83417i	0.0682761	−	0.542176i
$330$	23.1088	+	0.140858i	1.27210	+	0.00775396i
$331$	−10.7885	+	18.6862i	−0.592989	+	1.02709i	0.400838	+	0.916149i	$0.368719\pi$
$331$	−10.7885	+	18.6862i	−0.592989	+	1.02709i	−0.993827	+	0.110939i	$0.964614\pi$
$332$	2.87123	−	10.7156i	0.157579	−	0.588093i
$333$	−4.01958	−	0.745855i	−0.220271	−	0.0408726i
$334$	16.7601	+	9.67645i	0.917072	+	0.529472i
$335$	−0.972314	+	21.4679i	−0.0531232	+	1.17292i
$336$	4.30803	+	1.56233i	0.235022	+	0.0852322i
$337$	−1.09253	+	1.09253i	−0.0595139	+	0.0595139i	−0.736237	−	0.676723i	$-0.763399\pi$
$337$	−1.09253	+	1.09253i	−0.0595139	+	0.0595139i	0.676723	+	0.736237i	$0.263399\pi$
$338$	−0.461817	−	1.72352i	−0.0251195	−	0.0937474i
$339$	3.17908	−	14.0427i	0.172664	−	0.762693i
$340$	−1.88030	+	0.974936i	−0.101974	+	0.0528733i
$341$	−13.2985	−	7.67787i	−0.720152	−	0.415780i
$342$	9.51857	−	11.1401i	0.514705	−	0.602387i
$343$	16.9884	−	7.37533i	0.917286	−	0.398230i
$344$	−8.51458			−0.459075
$345$	−0.422354	+	0.721348i	−0.0227388	+	0.0388361i
$346$	−7.10384	−	12.3042i	−0.381905	−	0.661479i
$347$	4.18299	−	15.6111i	0.224555	−	0.838050i	−0.758028	−	0.652222i	$-0.773837\pi$
$347$	4.18299	−	15.6111i	0.224555	−	0.838050i	0.982582	−	0.185827i	$-0.0594965\pi$
$348$	1.92303	−	3.65415i	0.103085	−	0.195883i
$349$			23.5711i			1.26173i	0.775892	+	0.630866i	$0.217300\pi$
$349$			23.5711i			1.26173i	−0.775892	+	0.630866i	$0.782700\pi$
$350$	−4.00791	−	12.6070i	−0.214232	−	0.673873i
$351$	10.7776	−	13.6626i	0.575268	−	0.729253i
$352$	1.54432	+	5.76347i	0.0823124	+	0.307194i
$353$	26.1314	+	7.00188i	1.39083	+	0.372672i	0.875044	−	0.484044i	$-0.160832\pi$
$353$	26.1314	+	7.00188i	1.39083	+	0.372672i	0.515788	+	0.856716i	$0.327499\pi$
$354$	6.84565	+	1.54977i	0.363842	+	0.0823691i
$355$	23.4844	−	5.16628i	1.24642	−	0.274198i
$356$		−	0.377834i		−	0.0200252i
$357$	4.32458	+	0.373292i	0.228881	+	0.0197567i
$358$	6.12130	+	6.12130i	0.323521	+	0.323521i
$359$	3.59250	−	6.22240i	0.189605	−	0.328405i	−0.755514	−	0.655133i	$-0.772613\pi$
$359$	3.59250	−	6.22240i	0.189605	−	0.328405i	0.945119	+	0.326727i	$0.105946\pi$
$360$	−5.69540	+	3.54435i	−0.300174	+	0.186804i
$361$	2.42804	+	4.20549i	0.127791	+	0.221341i
$362$	−11.3162	+	3.03218i	−0.594768	+	0.159368i
$363$	−1.66852	−	42.5802i	−0.0875745	−	2.23488i
$364$	−5.35432	+	7.05982i	−0.280643	+	0.370035i
$365$	−29.6314	−	1.34205i	−1.55098	−	0.0702462i
$366$	6.88056	+	22.1672i	0.359652	+	1.15870i
$367$	−14.4270	−	3.86571i	−0.753084	−	0.201788i	−0.138198	−	0.990405i	$-0.544131\pi$
$367$	−14.4270	−	3.86571i	−0.753084	−	0.201788i	−0.614886	+	0.788616i	$0.710798\pi$
$368$	−0.208474	−	0.0558604i	−0.0108674	−	0.00291192i
$369$	−11.2490	−	5.36841i	−0.585602	−	0.279468i
$370$	−2.24995	+	2.05497i	−0.116969	+	0.106833i
$371$	9.90550	−	13.0607i	0.514268	−	0.678077i
$372$	4.45408	−	0.174534i	0.230933	−	0.00904919i
$373$	7.54451	−	2.02154i	0.390640	−	0.104672i	−0.0581526	−	0.998308i	$-0.518521\pi$
$373$	7.54451	−	2.02154i	0.390640	−	0.104672i	0.448792	+	0.893636i	$0.351854\pi$
$374$	2.82590	+	4.89460i	0.146124	+	0.253094i
$375$	18.1343	+	6.79304i	0.936454	+	0.350791i
$376$	−1.87316	+	3.24441i	−0.0966010	+	0.167318i
$377$	5.64560	+	5.64560i	0.290763	+	0.290763i
$378$	13.7473	+	0.106883i	0.707085	+	0.00549748i
$379$			17.2301i			0.885050i	0.896756	+	0.442525i	$0.145917\pi$
$379$			17.2301i			0.885050i	−0.896756	+	0.442525i	$0.854083\pi$
$380$	−2.34650	−	10.6665i	−0.120373	−	0.547180i
$381$	5.99336	−	26.4740i	0.307049	−	1.35630i
$382$	25.2869	+	6.77560i	1.29379	+	0.346670i
$383$	−1.41459	−	5.27933i	−0.0722823	−	0.269761i	0.920321	−	0.391164i	$-0.127927\pi$
$383$	−1.41459	−	5.27933i	−0.0722823	−	0.269761i	−0.992603	+	0.121403i	$0.961261\pi$
$384$	−1.27176	−	1.17585i	−0.0648993	−	0.0600049i
$385$	−33.1226	+	12.2060i	−1.68808	+	0.622073i
$386$			21.2830i			1.08327i
$387$	−24.0804	+	8.52163i	−1.22407	+	0.433179i
$388$	1.25433	−	4.68122i	0.0636789	−	0.237653i
$389$	2.33417	+	4.04291i	0.118347	+	0.204983i	0.919113	−	0.393994i	$-0.128907\pi$
$389$	2.33417	+	4.04291i	0.118347	+	0.204983i	−0.800766	+	0.598978i	$0.795574\pi$
$390$	−3.28060	−	12.5488i	−0.166120	−	0.635434i
$391$	−0.204434			−0.0103387
$392$	−6.99956	+	0.0788068i	−0.353531	+	0.00398035i
$393$	7.46646	−	0.292576i	0.376633	−	0.0147585i
$394$	−10.2837	−	5.93728i	−0.518084	−	0.299116i
$395$	0.682104	−	2.15115i	0.0343204	−	0.108236i
$396$	10.1358	+	14.7543i	0.509343	+	0.741430i
$397$	0.0132059	+	0.0492850i	0.000662783	+	0.00247354i	0.966256	−	0.257582i	$-0.0829258\pi$
$397$	0.0132059	+	0.0492850i	0.000662783	+	0.00247354i	−0.965594	+	0.260056i	$0.916259\pi$
$398$	−13.5115	+	13.5115i	−0.677273	+	0.677273i
$399$	−7.63085	+	21.0416i	−0.382020	+	1.05340i
$400$	−0.451988	+	4.97953i	−0.0225994	+	0.248976i
$401$	0.0554200	+	0.0319968i	0.00276754	+	0.00159784i	0.501383	−	0.865225i	$-0.332825\pi$
$401$	0.0554200	+	0.0319968i	0.00276754	+	0.00159784i	−0.498616	+	0.866823i	$0.666158\pi$
$402$	−14.0789	+	8.88108i	−0.702193	+	0.442948i
$403$	−2.23069	+	8.32505i	−0.111119	+	0.414700i
$404$	2.15580	−	3.73396i	0.107255	−	0.185771i
$405$	−12.5601	+	15.7240i	−0.624114	+	0.781333i
$406$	−0.788086	+	6.25813i	−0.0391121	+	0.310586i
$407$	5.74957	+	5.74957i	0.284996	+	0.284996i
$408$	−1.45184	−	0.764046i	−0.0718770	−	0.0378259i
$409$	29.6265	−	17.1049i	1.46494	−	0.845781i	0.465702	−	0.884942i	$-0.345802\pi$
$409$	29.6265	−	17.1049i	1.46494	−	0.845781i	0.999233	+	0.0391609i	$0.0124685\pi$
$410$	−8.24765	+	4.27641i	−0.407323	+	0.211197i
$411$	4.17404	+	13.4476i	0.205890	+	0.663321i
$412$	9.45212	−	9.45212i	0.465672	−	0.465672i
$413$	−10.6217	+	1.45925i	−0.522662	+	0.0718052i
$414$	−0.645498	+	0.0506659i	−0.0317245	+	0.00249009i
$415$	−20.8994	−	13.3623i	−1.02591	−	0.655928i
$416$	2.90030	−	1.67449i	0.142199	−	0.0820987i
$417$	−10.0950	−	16.0033i	−0.494353	−	0.783684i
$418$	−28.1504	+	7.54286i	−1.37688	+	0.368934i
$419$	−18.1904			−0.888658			−0.444329	−	0.895864i	$-0.646558\pi$
$419$	−18.1904			−0.888658			−0.444329	+	0.895864i	$0.646558\pi$
$420$	6.24174	−	8.12654i	0.304566	−	0.396535i
$421$	−2.01328			−0.0981212			−0.0490606	−	0.998796i	$-0.515623\pi$
$421$	−2.01328			−0.0981212			−0.0490606	+	0.998796i	$0.515623\pi$
$422$	−6.23274	+	1.67006i	−0.303405	+	0.0812972i
$423$	−2.05045	+	11.0503i	−0.0996964	+	0.537286i
$424$	−5.36557	+	3.09781i	−0.260575	+	0.150443i
$425$	0.807221	+	4.66675i	0.0391560	+	0.226370i
$426$	13.6761	+	12.6447i	0.662609	+	0.612638i
$427$	−21.7414	−	28.0061i	−1.05214	−	1.35531i
$428$	−11.1274	+	11.1274i	−0.537863	+	0.537863i
$429$	−33.0553	+	10.2601i	−1.59592	+	0.495364i
$430$	−5.75473	+	18.1486i	−0.277518	+	0.875205i
$431$	−35.3759	+	20.4243i	−1.70400	+	0.983804i	−0.762374	+	0.647136i	$0.775966\pi$
$431$	−35.3759	+	20.4243i	−1.70400	+	0.983804i	−0.941624	+	0.336667i	$0.890700\pi$
$432$	−4.77354	−	2.05265i	−0.229667	−	0.0987581i
$433$	7.07520	+	7.07520i	0.340012	+	0.340012i	0.856372	−	0.516360i	$-0.172713\pi$
$433$	7.07520	+	7.07520i	0.340012	+	0.340012i	−0.516360	+	0.856372i	$0.672713\pi$
$434$	−6.27587	+	2.64104i	−0.301251	+	0.126774i
$435$	−6.48903	−	6.56862i	−0.311125	−	0.314941i
$436$	5.29051	−	9.16343i	0.253370	−	0.438849i
$437$	0.272837	−	1.01824i	0.0130516	−	0.0487091i
$438$	−12.2582	−	19.4326i	−0.585722	−	0.928528i
$439$	−15.7197	−	9.07578i	−0.750261	−	0.433163i	0.0755273	−	0.997144i	$-0.475936\pi$
$439$	−15.7197	−	9.07578i	−0.750261	−	0.433163i	−0.825788	+	0.563980i	$0.809269\pi$
$440$	13.3285	+	0.603667i	0.635410	+	0.0287787i
$441$	−19.7168	+	7.22823i	−0.938896	+	0.344202i
$442$	2.24307	−	2.24307i	0.106692	−	0.106692i
$443$	2.15250	+	8.03323i	0.102268	+	0.381670i	0.998021	−	0.0628823i	$-0.0200293\pi$
$443$	2.15250	+	8.03323i	0.102268	+	0.381670i	−0.895753	+	0.444553i	$0.853363\pi$
$444$	−2.30206	−	0.521157i	−0.109251	−	0.0247330i
$445$	−0.805345	−	0.255366i	−0.0381770	−	0.0121055i
$446$	−8.01090	−	4.62509i	−0.379327	−	0.219004i
$447$	0.795034	+	20.2891i	0.0376038	+	0.959640i
$448$	2.45002	+	0.998710i	0.115752	+	0.0471846i
$449$	12.4820			0.589061			0.294531	−	0.955642i	$-0.404837\pi$
$449$	12.4820			0.589061			0.294531	+	0.955642i	$0.404837\pi$
$450$	3.70537	+	14.5351i	0.174673	+	0.685193i
$451$	12.3954	+	21.4694i	0.583676	+	1.01096i
$452$	2.15149	−	8.02946i	0.101197	−	0.377674i
$453$	25.2674	+	13.2972i	1.18717	+	0.624757i
$454$			9.82300i			0.461016i
$455$	11.4290	+	16.1841i	0.535801	+	0.758723i
$456$	5.74317	−	6.21162i	0.268949	−	0.290886i
$457$	8.18804	+	30.5582i	0.383021	+	1.42945i	0.841264	+	0.540625i	$0.181812\pi$
$457$	8.18804	+	30.5582i	0.383021	+	1.42945i	−0.458243	+	0.888827i	$0.651521\pi$
$458$	8.78434	+	2.35376i	0.410465	+	0.109984i
$459$	−4.87069	−	0.707777i	−0.227344	−	0.0330362i
$460$	−0.259966	+	0.406603i	−0.0121210	+	0.0189580i
$461$			13.2219i			0.615807i	0.951418	+	0.307904i	$0.0996274\pi$
$461$			13.2219i			0.615807i	−0.951418	+	0.307904i	$0.900373\pi$
$462$	−22.4165	−	15.6574i	−1.04291	−	0.728449i
$463$	−16.2332	−	16.2332i	−0.754422	−	0.754422i	0.220879	−	0.975301i	$-0.429107\pi$
$463$	−16.2332	−	16.2332i	−0.754422	−	0.754422i	−0.975301	+	0.220879i	$0.929107\pi$
$464$	1.19202	−	2.06463i	0.0553380	−	0.0958482i
$465$	2.63835	−	9.61174i	0.122351	−	0.445734i
$466$	9.35245	+	16.1989i	0.433244	+	0.750401i
$467$	12.6067	−	3.37796i	0.583369	−	0.156313i	0.0449484	−	0.998989i	$-0.485688\pi$
$467$	12.6067	−	3.37796i	0.583369	−	0.156313i	0.538421	+	0.842676i	$0.319021\pi$
$468$	6.52657	−	7.63839i	0.301691	−	0.353085i
$469$	15.3653	−	20.2596i	0.709503	−	0.935500i
$470$	5.64939	+	6.18540i	0.260587	+	0.285311i
$471$	4.16253	−	1.29202i	0.191799	−	0.0595332i
$472$	3.91427	+	1.04883i	0.180169	+	0.0482761i
$473$	49.0735	+	13.1492i	2.25640	+	0.604602i
$474$	1.66946	−	0.518189i	0.0766808	−	0.0238012i
$475$	−24.3214	−	2.20763i	−1.11594	−	0.101293i
$476$	2.48644	+	0.313117i	0.113966	+	0.0143517i
$477$	−12.0742	+	14.1310i	−0.552838	+	0.647016i
$478$	8.57446	−	2.29752i	0.392187	−	0.105086i
$479$	15.7131	+	27.2159i	0.717951	+	1.24353i	0.961810	+	0.273717i	$0.0882532\pi$
$479$	15.7131	+	27.2159i	0.717951	+	1.24353i	−0.243859	+	0.969811i	$0.578414\pi$
$480$	−3.36584	+	1.91601i	−0.153629	+	0.0874536i
$481$	2.28188	−	3.95233i	0.104045	−	0.180211i
$482$	2.91802	+	2.91802i	0.132912	+	0.132912i
$483$	0.895896	−	0.419030i	0.0407647	−	0.0190665i
$484$		−	24.6026i		−	1.11830i
$485$	−9.13016	−	5.83746i	−0.414579	−	0.265066i
$486$	−15.5545	−	1.02767i	−0.705569	−	0.0466161i
$487$	−25.7118	−	6.88945i	−1.16511	−	0.312191i	−0.376106	−	0.926577i	$-0.622737\pi$
$487$	−25.7118	−	6.88945i	−1.16511	−	0.312191i	−0.789006	+	0.614386i	$0.789404\pi$
$488$	3.46833	+	12.9440i	0.157004	+	0.585946i
$489$	−5.92295	+	6.40607i	−0.267845	+	0.289692i
$490$	−4.56280	+	14.9727i	−0.206126	+	0.676396i
$491$		−	17.2123i		−	0.776779i	−0.921495	−	0.388389i	$-0.873032\pi$
$491$		−	17.2123i		−	0.776779i	0.921495	−	0.388389i	$-0.126968\pi$
$492$	−6.36829	−	3.35137i	−0.287105	−	0.151092i
$493$	0.584460	−	2.18123i	0.0263227	−	0.0982378i
$494$	8.17866	+	14.1659i	0.367975	+	0.637352i
$495$	38.2989	−	11.6323i	1.72141	−	0.522832i
$496$	2.57354			0.115555
$497$	−26.3467	−	10.7398i	−1.18181	−	0.481746i
$498$	−0.752354	−	19.1999i	−0.0337138	−	0.860368i
$499$	−34.9854	−	20.1988i	−1.56616	−	0.904224i	−0.996610	−	0.0822678i	$-0.973784\pi$
$499$	−34.9854	−	20.1988i	−1.56616	−	0.904224i	−0.569551	−	0.821956i	$-0.692883\pi$
$500$	10.3083	+	4.32891i	0.461000	+	0.193595i
$501$	32.6929	+	7.40125i	1.46061	+	0.330663i
$502$	−2.51677	−	9.39273i	−0.112329	−	0.419218i
$503$	−3.72801	+	3.72801i	−0.166224	+	0.166224i	−0.785317	−	0.619094i	$-0.787500\pi$
$503$	−3.72801	+	3.72801i	−0.166224	+	0.166224i	0.619094	+	0.785317i	$0.287500\pi$
$504$	7.92851	+	0.372438i	0.353164	+	0.0165897i
$505$	−6.50182	−	7.11871i	−0.289327	−	0.316779i
$506$	1.11527	+	0.643900i	0.0495797	+	0.0286248i
$507$	−1.64888	−	2.61393i	−0.0732295	−	0.116089i
$508$	4.05609	−	15.1375i	0.179960	−	0.671620i
$509$	4.53149	−	7.84877i	0.200855	−	0.347891i	−0.747949	−	0.663756i	$-0.768961\pi$
$509$	4.53149	−	7.84877i	0.200855	−	0.347891i	0.948804	+	0.315865i	$0.102295\pi$
$510$	−2.60980	+	2.57818i	−0.115564	+	0.114164i
$511$	27.9636	+	21.2082i	1.23704	+	0.938195i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	10.0257	−	23.3152i	0.442645	−	1.02939i
$514$	−5.44728	+	3.14499i	−0.240269	+	0.138719i
$515$	−13.7586	−	26.5354i	−0.606276	−	1.16929i
$516$	−14.0848	+	4.37183i	−0.620048	+	0.192459i
$517$	15.8063	−	15.8063i	0.695162	−	0.695162i
$518$	3.57189	−	0.490720i	0.156940	−	0.0215610i
$519$	−18.0688	−	16.7061i	−0.793131	−	0.733317i
$520$	−1.60892	−	7.31367i	−0.0705558	−	0.320726i
$521$	−28.4540	+	16.4279i	−1.24659	+	0.719721i	−0.970428	−	0.241389i	$-0.922397\pi$
$521$	−28.4540	+	16.4279i	−1.24659	+	0.719721i	−0.276165	+	0.961110i	$0.589064\pi$
$522$	1.30484	−	7.03206i	0.0571112	−	0.307785i
$523$	11.2645	−	3.01831i	0.492561	−	0.131981i	−0.00398437	−	0.999992i	$-0.501268\pi$
$523$	11.2645	−	3.01831i	0.492561	−	0.131981i	0.496545	+	0.868011i	$0.334602\pi$
$524$	4.31407			0.188461
$525$	−13.1030	−	18.7966i	−0.571860	−	0.820351i
$526$	−12.9960			−0.566654
$527$	2.35462	−	0.630917i	0.102569	−	0.0274832i
$528$	5.51387	+	8.74099i	0.239961	+	0.380403i
$529$	19.8782	−	11.4767i	0.864271	−	0.498987i
$530$	2.97650	+	13.5303i	0.129291	+	0.587719i
$531$	12.1198	−	0.951296i	0.525954	−	0.0412827i
$532$	−4.87797	+	11.9665i	−0.211487	+	0.518815i
$533$	9.83891	−	9.83891i	0.426170	−	0.426170i
$534$	−0.194000	−	0.625012i	−0.00839519	−	0.0270469i
$535$	16.1972	+	31.2385i	0.700264	+	1.35056i
$536$	−8.32300	+	4.80529i	−0.359499	+	0.207557i
$537$	13.2688	+	6.98284i	0.572592	+	0.301332i
$538$	−7.77555	−	7.77555i	−0.335228	−	0.335228i
$539$	40.4635	+	10.3553i	1.74288	+	0.446036i
$540$	−7.60146	+	8.78737i	−0.327115	+	0.378148i
$541$	−1.99471	+	3.45495i	−0.0857595	+	0.148540i	−0.905715	−	0.423888i	$-0.860665\pi$
$541$	−1.99471	+	3.45495i	−0.0857595	+	0.148540i	0.819955	+	0.572428i	$0.193998\pi$
$542$	4.96646	−	18.5351i	0.213328	−	0.796150i
$543$	−17.1624	+	10.8262i	−0.736509	+	0.464595i
$544$	−0.820307	−	0.473605i	−0.0351704	−	0.0203056i
$545$	−15.9560	−	17.4699i	−0.683479	−	0.748328i
$546$	−5.23222	+	14.4275i	−0.223918	+	0.617440i
$547$	−9.65788	+	9.65788i	−0.412941	+	0.412941i	−0.882762	−	0.469821i	$-0.844319\pi$
$547$	−9.65788	+	9.65788i	−0.412941	+	0.412941i	0.469821	+	0.882762i	$0.344319\pi$
$548$	2.10404	+	7.85237i	0.0898800	+	0.335437i
$549$	22.7636	+	33.1361i	0.971526	+	1.41421i
$550$	10.2950	−	28.0014i	0.438980	−	1.19398i
$551$	10.0842	+	5.82213i	0.429602	+	0.248031i
$552$	−0.373538	+	0.0146372i	−0.0158988	+	0.000623001i
$553$	−2.10920	+	1.63739i	−0.0896923	+	0.0696290i
$554$	1.72041			0.0730934
$555$	−2.66673	+	4.55457i	−0.113196	+	0.193331i
$556$	−5.46209	−	9.46062i	−0.231644	−	0.401220i
$557$	1.21720	−	4.54267i	0.0515746	−	0.192479i	−0.935332	−	0.353771i	$-0.884899\pi$
$557$	1.21720	−	4.54267i	0.0515746	−	0.192479i	0.986907	+	0.161292i	$0.0515660\pi$
$558$	7.27831	−	2.57567i	0.308115	−	0.109037i
$559$		−	28.5152i		−	1.20606i
$560$	3.78462	−	4.54716i	0.159929	−	0.192153i
$561$	7.18773	+	6.64567i	0.303466	+	0.280580i
$562$	−4.58965	−	17.1288i	−0.193603	−	0.722536i
$563$	−25.7242	−	6.89278i	−1.08415	−	0.290496i	−0.327853	−	0.944729i	$-0.606325\pi$
$563$	−25.7242	−	6.89278i	−1.08415	−	0.290496i	−0.756293	+	0.654233i	$0.772992\pi$
$564$	−1.43273	+	6.32868i	−0.0603288	+	0.266485i
$565$	−15.6605	−	10.0127i	−0.658842	−	0.421238i
$566$		−	16.6455i		−	0.699665i
$567$	22.7956	−	6.88178i	0.957327	−	0.289008i
$568$	7.60399	+	7.60399i	0.319057	+	0.319057i
$569$	2.30517	−	3.99267i	0.0966376	−	0.167381i	−0.813653	−	0.581350i	$-0.802525\pi$
$569$	2.30517	−	3.99267i	0.0966376	−	0.167381i	0.910291	+	0.413969i	$0.135858\pi$
$570$	−9.35831	−	16.4397i	−0.391977	−	0.688582i
$571$	−2.42916	−	4.20743i	−0.101657	−	0.176075i	0.810710	−	0.585447i	$-0.199081\pi$
$571$	−2.42916	−	4.20743i	−0.101657	−	0.176075i	−0.912368	+	0.409372i	$0.865748\pi$
$572$	−19.3018	+	5.17189i	−0.807047	+	0.216248i
$573$	45.3084	−	1.77543i	1.89279	−	0.0741695i
$574$	10.9064	+	1.37344i	0.455225	+	0.0573264i
$575$	0.690963	+	0.828922i	0.0288152	+	0.0345684i
$576$	−2.70749	−	1.29210i	−0.112812	−	0.0538375i
$577$	−13.0720	−	3.50264i	−0.544196	−	0.145817i	−0.0237602	−	0.999718i	$-0.507564\pi$
$577$	−13.0720	−	3.50264i	−0.544196	−	0.145817i	−0.520436	+	0.853901i	$0.674230\pi$
$578$	15.5541	+	4.16771i	0.646965	+	0.173354i
$579$	10.9278	+	35.2062i	0.454143	+	1.46312i
$580$	−3.59508	−	3.93618i	−0.149277	−	0.163441i
$581$	11.3845	+	27.0530i	0.472310	+	1.12235i
$582$	−0.328674	−	8.38770i	−0.0136240	−	0.347681i
$583$	35.7083	−	9.56802i	1.47889	−	0.396267i
$584$	−6.63257	−	11.4880i	−0.274458	−	0.475375i
$585$	−11.8700	−	19.0738i	−0.490763	−	0.788604i
$586$	−4.05653	+	7.02612i	−0.167574	+	0.290246i
$587$	20.4866	+	20.4866i	0.845574	+	0.845574i	0.989577	−	0.144004i	$-0.0459977\pi$
$587$	20.4866	+	20.4866i	0.845574	+	0.845574i	−0.144004	+	0.989577i	$0.545998\pi$
$588$	−11.5382	+	3.72430i	−0.475827	+	0.153587i
$589$			12.5698i			0.517931i
$590$	4.88108	−	7.63432i	0.200951	−	0.314300i
$591$	−20.0597	−	4.54126i	−0.825146	−	0.186802i
$592$	−1.31630	−	0.352701i	−0.0540994	−	0.0144959i
$593$	−8.84754	−	33.0195i	−0.363325	−	1.35595i	−0.869678	−	0.493620i	$-0.835673\pi$
$593$	−8.84754	−	33.0195i	−0.363325	−	1.35595i	0.506353	−	0.862326i	$-0.330993\pi$
$594$	24.3422	+	19.2022i	0.998773	+	0.787877i
$595$	2.34791	−	5.08817i	0.0962549	−	0.208595i
$596$			11.7229i			0.480188i
$597$	−15.4132	+	29.2883i	−0.630821	+	1.19869i
$598$	0.187075	−	0.698175i	0.00765008	−	0.0285505i
$599$	−20.2161	−	35.0153i	−0.826006	−	1.43068i	−0.901148	−	0.433512i	$-0.857274\pi$
$599$	−20.2161	−	35.0153i	−0.826006	−	1.43068i	0.0751420	−	0.997173i	$-0.476059\pi$
$600$	1.80907	+	8.46919i	0.0738550	+	0.345753i
$601$	20.3443			0.829861			0.414931	−	0.909853i	$-0.363806\pi$
$601$	20.3443			0.829861			0.414931	+	0.909853i	$0.363806\pi$
$602$	17.7948	−	13.8142i	0.725260	−	0.563026i
$603$	−18.7293	+	21.9199i	−0.762716	+	0.892647i
$604$	14.2764	+	8.24246i	0.580897	+	0.335381i
$605$	−52.4398	−	16.6281i	−2.13198	−	0.676028i
$606$	1.64891	−	7.28361i	0.0669825	−	0.295876i
$607$	11.9417	+	44.5671i	0.484699	+	1.80892i	0.581413	+	0.813609i	$0.302500\pi$
$607$	11.9417	+	44.5671i	0.484699	+	1.80892i	−0.0967136	+	0.995312i	$0.530833\pi$
$608$	3.45370	−	3.45370i	0.140066	−	0.140066i
$609$	1.90960	+	10.7568i	0.0773809	+	0.435889i
$610$	29.9339	+	1.35575i	1.21199	+	0.0548928i
$611$	−10.8655	−	6.27319i	−0.439570	−	0.253786i
$612$	−2.79394	−	0.518430i	−0.112938	−	0.0209563i
$613$	3.99730	−	14.9181i	0.161450	−	0.602538i	−0.837017	−	0.547177i	$-0.815702\pi$
$613$	3.99730	−	14.9181i	0.161450	−	0.602538i	0.998466	−	0.0553608i	$-0.0176309\pi$
$614$	1.12009	−	1.94006i	0.0452032	−	0.0782943i
$615$	−11.4475	+	11.3088i	−0.461608	+	0.456015i
$616$	−12.5783	−	9.53964i	−0.506793	−	0.384363i
$617$	2.50025	+	2.50025i	0.100656	+	0.100656i	0.755642	−	0.654985i	$-0.227325\pi$
$617$	2.50025	+	2.50025i	0.100656	+	0.100656i	−0.654985	+	0.755642i	$0.727325\pi$
$618$	10.7825	−	20.4889i	0.433734	−	0.824183i
$619$	4.86025	−	2.80606i	0.195350	−	0.112785i	−0.399135	−	0.916892i	$-0.630689\pi$
$619$	4.86025	−	2.80606i	0.195350	−	0.112785i	0.594485	+	0.804107i	$0.297356\pi$
$620$	1.73937	−	5.48544i	0.0698548	−	0.220301i
$621$	−1.04177	+	0.415244i	−0.0418047	+	0.0166632i
$622$	4.24964	−	4.24964i	0.170395	−	0.170395i
$623$	0.613006	+	0.789641i	0.0245596	+	0.0316363i
$624$	3.93790	−	4.25910i	0.157642	−	0.170501i
$625$	16.1940	−	19.0461i	0.647761	−	0.761844i
$626$	−2.78376	+	1.60721i	−0.111261	+	0.0642369i
$627$	−42.6933	+	26.9312i	−1.70501	+	1.07553i
$628$	2.43060	−	0.651278i	0.0969916	−	0.0259888i
$629$	−1.29079			−0.0514672
$630$	6.15247	−	16.6477i	0.245120	−	0.663262i
$631$	20.0318			0.797455			0.398727	−	0.917069i	$-0.369452\pi$
$631$	20.0318			0.797455			0.398727	+	0.917069i	$0.369452\pi$
$632$	0.974838	−	0.261207i	0.0387770	−	0.0103903i
$633$	−9.45269	+	5.96282i	−0.375711	+	0.237001i
$634$	−0.681432	+	0.393425i	−0.0270631	+	0.0156249i
$635$	−29.5240	−	18.8765i	−1.17162	−	0.749090i
$636$	−7.28513	+	7.87935i	−0.288874	+	0.312437i
$637$	−0.263923	−	23.4414i	−0.0104570	−	0.928781i
$638$	−10.0586	+	10.0586i	−0.398224	+	0.398224i
$639$	29.1154	+	13.8948i	1.15179	+	0.549671i
$640$	−1.98509	+	1.02927i	−0.0784677	+	0.0406856i
$641$	−32.1479	+	18.5606i	−1.26977	+	0.733100i	−0.974944	−	0.222452i	$-0.928594\pi$
$641$	−32.1479	+	18.5606i	−1.26977	+	0.733100i	−0.294823	+	0.955552i	$0.595261\pi$
$642$	−12.6935	+	24.1203i	−0.500973	+	0.951952i
$643$	−7.70403	−	7.70403i	−0.303817	−	0.303817i	0.538688	−	0.842505i	$-0.318920\pi$
$643$	−7.70403	−	7.70403i	−0.303817	−	0.303817i	−0.842505	+	0.538688i	$0.818920\pi$
$644$	0.526322	−	0.221489i	0.0207400	−	0.00872788i
$645$	−0.201003	+	32.9762i	−0.00791450	+	1.29844i
$646$	2.31321	−	4.00660i	0.0910121	−	0.157638i
$647$	6.17291	−	23.0376i	0.242682	−	0.905702i	−0.731852	−	0.681464i	$-0.761344\pi$
$647$	6.17291	−	23.0376i	0.242682	−	0.905702i	0.974534	−	0.224239i	$-0.0719895\pi$
$648$	−8.95030	−	0.944502i	−0.351601	−	0.0371035i
$649$	−20.9401	−	12.0898i	−0.821970	−	0.474565i
$650$	−16.6763	−	1.51370i	−0.654100	−	0.0593722i
$651$	−9.02548	+	7.59115i	−0.353736	+	0.297521i
$652$	−3.56181	+	3.56181i	−0.139491	+	0.139491i
$653$	5.34683	+	19.9547i	0.209238	+	0.780886i	0.988116	+	0.153711i	$0.0491224\pi$
$653$	5.34683	+	19.9547i	0.209238	+	0.780886i	−0.778878	+	0.627175i	$0.784211\pi$
$654$	4.04656	−	17.8745i	0.158233	−	0.698950i
$655$	2.91574	−	9.19535i	0.113928	−	0.359292i
$656$	−3.59815	−	2.07740i	−0.140484	−	0.0811087i
$657$	−30.2553	−	25.8514i	−1.18037	−	1.00856i
$658$	−1.34905	−	9.81961i	−0.0525916	−	0.382808i
$659$	−15.8694			−0.618184			−0.309092	−	0.951032i	$-0.600025\pi$
$659$	−15.8694			−0.618184			−0.309092	+	0.951032i	$0.600025\pi$
$660$	22.3579	−	5.84495i	0.870279	−	0.227514i
$661$	−2.27276	−	3.93654i	−0.0884003	−	0.153114i	0.818435	−	0.574599i	$-0.194842\pi$
$661$	−2.27276	−	3.93654i	−0.0884003	−	0.153114i	−0.906835	+	0.421486i	$0.861509\pi$
$662$	−5.58454	+	20.8418i	−0.217049	+	0.810039i
$663$	2.55878	−	4.86220i	0.0993746	−	0.188832i
$664$		−	11.0936i		−	0.430514i
$665$	22.2096	+	18.4851i	0.861250	+	0.716821i
$666$	−4.07565	+	0.319903i	−0.157928	+	0.0123960i
$667$	−0.133173	−	0.497008i	−0.00515648	−	0.0192442i
$668$	18.6935	+	5.00890i	0.723272	+	0.193800i
$669$	−15.6264	−	3.53760i	−0.604150	−	0.136772i
$670$	4.61712	+	20.9880i	0.178375	+	0.810839i
$671$		−	79.9584i		−	3.08676i
$672$	4.56560	+	0.394096i	0.176122	+	0.0152026i
$673$	−8.60027	−	8.60027i	−0.331516	−	0.331516i	0.521646	−	0.853162i	$-0.325318\pi$
$673$	−8.60027	−	8.60027i	−0.331516	−	0.331516i	−0.853162	+	0.521646i	$0.825318\pi$
$674$	−0.772535	+	1.33807i	−0.0297570	+	0.0515405i
$675$	13.5925	+	22.1414i	0.523176	+	0.852225i
$676$	−0.892162	−	1.54527i	−0.0343139	−	0.0594335i
$677$	37.4764	−	10.0418i	1.44033	−	0.385936i	0.547683	−	0.836686i	$-0.315510\pi$
$677$	37.4764	−	10.0418i	1.44033	−	0.385936i	0.892650	+	0.450750i	$0.148843\pi$
$678$	−0.563759	−	14.3870i	−0.0216510	−	0.552529i
$679$	4.97347	+	11.8184i	0.190864	+	0.453549i
$680$	−1.56390	+	1.42837i	−0.0599727	+	0.0547756i
$681$	5.04364	+	16.2492i	0.193273	+	0.622670i
$682$	−14.8325	−	3.97436i	−0.567966	−	0.152186i
$683$	9.11142	+	2.44140i	0.348639	+	0.0934175i	0.428889	−	0.903357i	$-0.358905\pi$
$683$	9.11142	+	2.44140i	0.348639	+	0.0934175i	−0.0802500	+	0.996775i	$0.525572\pi$
$684$	6.31096	−	13.2241i	0.241306	−	0.505636i
$685$	18.1592	+	0.822459i	0.693828	+	0.0314245i
$686$	14.5006	−	11.5209i	0.553636	−	0.439871i
$687$	15.7396	−	0.616760i	0.600502	−	0.0235309i
$688$	−8.22445	+	2.20373i	−0.313554	+	0.0840166i
$689$	−10.3745	−	17.9692i	−0.395238	−	0.684571i
$690$	−0.221264	+	0.806082i	−0.00842337	+	0.0306870i
$691$	−5.48550	+	9.50117i	−0.208678	+	0.361441i	−0.951298	−	0.308271i	$-0.900250\pi$
$691$	−5.48550	+	9.50117i	−0.208678	+	0.361441i	0.742620	+	0.669713i	$0.233583\pi$
$692$	−10.0464	−	10.0464i	−0.381905	−	0.381905i
$693$	−45.1206	−	14.3907i	−1.71399	−	0.546657i
$694$		−	16.1618i		−	0.613495i
$695$	−23.8568	+	5.24820i	−0.904939	+	0.199076i
$696$	0.911740	−	4.02735i	0.0345594	−	0.152656i
$697$	−3.80136	−	1.01857i	−0.143987	−	0.0385811i
$698$	6.10064	+	22.7679i	0.230913	+	0.861778i
$699$	23.7882	+	21.9942i	0.899751	+	0.831896i
$700$	−7.13428	−	11.1401i	−0.269650	−	0.421057i
$701$		−	10.6209i		−	0.401147i	−0.979679	−	0.200574i	$-0.935719\pi$
$701$		−	10.6209i		−	0.401147i	0.979679	−	0.200574i	$-0.0642806\pi$
$702$	6.87428	−	15.9865i	0.259453	−	0.603371i
$703$	1.72268	−	6.42914i	0.0649723	−	0.242480i
$704$	2.98339	+	5.16739i	0.112441	+	0.194753i
$705$	12.5211	+	7.33118i	0.471572	+	0.276108i
$706$	27.0532			1.01816
$707$	1.55261	+	11.3013i	0.0583919	+	0.425028i
$708$	7.01350	−	0.274826i	0.263583	−	0.0103286i
$709$	8.79213	+	5.07614i	0.330196	+	0.190638i	0.655928	−	0.754824i	$-0.272278\pi$
$709$	8.79213	+	5.07614i	0.330196	+	0.190638i	−0.325732	+	0.945462i	$0.605611\pi$
$710$	21.3471	−	11.0685i	0.801141	−	0.415392i
$711$	2.49555	−	1.71437i	0.0935904	−	0.0642941i
$712$	−0.0977906	−	0.364960i	−0.00366486	−	0.0136774i
$713$	0.392756	−	0.392756i	0.0147088	−	0.0147088i
$714$	4.27384	−	0.758711i	0.159944	−	0.0283940i
$715$	−2.02167	+	44.6368i	−0.0756062	+	1.66932i
$716$	7.49703	+	4.32841i	0.280177	+	0.161760i
$717$	13.0042	−	8.20312i	0.485650	−	0.306351i
$718$	1.85962	−	6.94018i	0.0694002	−	0.259005i
$719$	−14.4032	+	24.9471i	−0.537150	+	0.930370i	0.461906	+	0.886929i	$0.347166\pi$
$719$	−14.4032	+	24.9471i	−0.537150	+	0.930370i	−0.999056	+	0.0434417i	$0.986168\pi$
$720$	−4.58399	+	4.89766i	−0.170835	+	0.182525i
$721$	−4.41881	+	35.0894i	−0.164565	+	1.30680i
$722$	3.43376	+	3.43376i	0.127791	+	0.127791i
$723$	6.32525	+	3.32872i	0.235239	+	0.123796i
$724$	−10.1459	+	5.85771i	−0.377068	+	0.217700i
$725$	−10.8197	+	5.00249i	−0.401833	+	0.185788i
$726$	−12.6322	−	40.6975i	−0.468826	−	1.51042i
$727$	0.151969	−	0.151969i	0.00563622	−	0.00563622i	−0.704283	−	0.709919i	$-0.748731\pi$
$727$	0.151969	−	0.151969i	0.00563622	−	0.00563622i	0.709919	+	0.704283i	$0.248731\pi$
$728$	−3.34466	+	8.20506i	−0.123961	+	0.304100i
$729$	−26.2579	+	6.28654i	−0.972516	+	0.232835i
$730$	−28.9691	+	6.37285i	−1.07219	+	0.235870i
$731$	−6.98457	+	4.03254i	−0.258334	+	0.149149i
$732$	12.3834	+	19.6311i	0.457704	+	0.725584i
$733$	−33.0589	+	8.85810i	−1.22106	+	0.327181i	−0.811091	−	0.584919i	$-0.801126\pi$
$733$	−33.0589	+	8.85810i	−1.22106	+	0.327181i	−0.409966	+	0.912101i	$0.634459\pi$
$734$	−14.9359			−0.551296
$735$	0.139974	+	27.1105i	0.00516301	+	0.999987i
$736$	−0.215828			−0.00795552
$737$	55.3903	−	14.8418i	2.04033	−	0.546704i
$738$	−12.2552	−	2.27402i	−0.451119	−	0.0837077i
$739$	28.3705	−	16.3797i	1.04362	−	0.602537i	0.122767	−	0.992436i	$-0.460823\pi$
$739$	28.3705	−	16.3797i	1.04362	−	0.602537i	0.920858	+	0.389899i	$0.127490\pi$
$740$	−1.64142	+	2.56728i	−0.0603397	+	0.0943750i
$741$	20.8026	+	19.2338i	0.764203	+	0.706570i
$742$	6.18763	−	15.1794i	0.227155	−	0.557253i
$743$	0.701038	−	0.701038i	0.0257186	−	0.0257186i	−0.694131	−	0.719849i	$-0.744211\pi$
$743$	0.701038	−	0.701038i	0.0257186	−	0.0257186i	0.719849	+	0.694131i	$0.244211\pi$
$744$	4.25714	−	1.32139i	0.156074	−	0.0484444i
$745$	24.9871	+	7.92313i	0.915456	+	0.290281i
$746$	6.76422	−	3.90532i	0.247656	−	0.142984i
$747$	−11.1028	−	31.3741i	−0.406229	−	1.14792i
$748$	3.99642	+	3.99642i	0.146124	+	0.146124i
$749$	5.20199	−	41.3086i	0.190077	−	1.50938i
$750$	19.2746	+	1.86806i	0.703809	+	0.0682120i
$751$	−0.934185	+	1.61806i	−0.0340889	+	0.0590437i	−0.882567	−	0.470188i	$-0.844186\pi$
$751$	−0.934185	+	1.61806i	−0.0340889	+	0.0590437i	0.848478	+	0.529231i	$0.177520\pi$
$752$	−0.969620	+	3.61867i	−0.0353584	+	0.131959i
$753$	−8.98595	−	14.2452i	−0.327466	−	0.519123i
$754$	6.91442	+	3.99204i	0.251808	+	0.145382i
$755$	27.2176	−	24.8589i	0.990548	−	0.904709i
$756$	13.3065	−	3.45482i	0.483954	−	0.125651i
$757$	15.1882	−	15.1882i	0.552024	−	0.552024i	−0.375001	−	0.927025i	$-0.622358\pi$
$757$	15.1882	−	15.1882i	0.552024	−	0.552024i	0.927025	+	0.375001i	$0.122358\pi$
$758$	4.45947	+	16.6430i	0.161975	+	0.604500i
$759$	2.17548	+	0.492501i	0.0789650	+	0.0178766i
$760$	−5.02724	−	9.69573i	−0.182357	−	0.351701i
$761$	43.5861	+	25.1645i	1.58000	+	0.912211i	0.994858	+	0.101277i	$0.0322929\pi$
$761$	43.5861	+	25.1645i	1.58000	+	0.912211i	0.585138	+	0.810934i	$0.301040\pi$
$762$	−1.06283	−	27.1231i	−0.0385022	−	0.982566i
$763$	3.81023	+	27.7342i	0.137940	+	1.00405i
$764$	26.1789			0.947120
$765$	−2.99336	+	5.60482i	−0.108225	+	0.202643i
$766$	−2.73278	−	4.73332i	−0.0987395	−	0.171022i
$767$	−3.51250	+	13.1088i	−0.126829	+	0.473332i
$768$	−1.53276	−	0.806628i	−0.0553087	−	0.0291067i
$769$			5.32307i			0.191955i	0.995384	+	0.0959775i	$0.0305977\pi$
$769$			5.32307i			0.191955i	−0.995384	+	0.0959775i	$0.969402\pi$
$770$	−28.8348	+	20.3628i	−1.03913	+	0.733824i
$771$	−7.39607	+	7.99934i	−0.266363	+	0.288089i
$772$	5.50843	+	20.5578i	0.198253	+	0.739890i
$773$	18.9649	+	5.08164i	0.682121	+	0.182774i	0.583209	−	0.812322i	$-0.301797\pi$
$773$	18.9649	+	5.08164i	0.682121	+	0.182774i	0.0989124	+	0.995096i	$0.468464\pi$
$774$	−21.0543	+	14.4637i	−0.756781	+	0.519888i
$775$	−10.5165	−	7.41487i	−0.377764	−	0.266350i
$776$		−	4.84635i		−	0.173974i
$777$	5.65666	−	2.64574i	0.202931	−	0.0949155i
$778$	3.30102	+	3.30102i	0.118347	+	0.118347i
$779$	10.1466	−	17.5744i	0.363538	−	0.629667i
$780$	−6.41669	−	11.2721i	−0.229754	−	0.403608i
$781$	−32.0824	−	55.5684i	−1.14800	−	1.98839i
$782$	−0.197468	+	0.0529115i	−0.00706145	+	0.00189211i
$783$	−1.45217	−	12.3024i	−0.0518963	−	0.439652i
$784$	−6.74066	+	1.88774i	−0.240738	+	0.0674193i
$785$	0.254582	−	5.62096i	0.00908641	−	0.200620i
$786$	7.13632	−	2.21507i	0.254544	−	0.0790089i
$787$	21.4421	+	5.74540i	0.764329	+	0.204801i	0.619865	−	0.784709i	$-0.287187\pi$
$787$	21.4421	+	5.74540i	0.764329	+	0.204801i	0.144464	+	0.989510i	$0.453854\pi$
$788$	−11.4699	−	3.07336i	−0.408600	−	0.109484i
$789$	−21.4980	+	6.67284i	−0.765349	+	0.237559i
$790$	0.102105	−	2.25439i	0.00363272	−	0.0802075i
$791$	8.53074	+	20.2715i	0.303318	+	0.720772i
$792$	13.6091	+	11.6282i	0.483579	+	0.413190i
$793$	−43.3491	+	11.6154i	−1.53937	+	0.412473i
$794$	0.0255118	+	0.0441877i	0.000905379	+	0.00156816i
$795$	11.8709	+	20.8535i	0.421017	+	0.739597i
$796$	−9.55411	+	16.5482i	−0.338636	+	0.586535i
$797$	−0.507697	−	0.507697i	−0.0179836	−	0.0179836i	0.698058	−	0.716041i	$-0.254048\pi$
$797$	−0.507697	−	0.507697i	−0.0179836	−	0.0179836i	−0.716041	+	0.698058i	$0.754048\pi$
$798$	−1.92487	+	22.2996i	−0.0681397	+	0.789398i
$799$			3.54855i			0.125539i
$800$	0.852210	+	4.92684i	0.0301302	+	0.174190i
$801$	−0.641827	−	0.934283i	−0.0226778	−	0.0330113i
$802$	0.0618130	+	0.0165627i	0.00218269	+	0.000584851i
$803$	20.4856	+	76.4533i	0.722921	+	2.69798i
$804$	−11.3006	+	12.2224i	−0.398541	+	0.431049i
$805$	−0.116375	−	1.27154i	−0.00410167	−	0.0448159i
$806$			8.61873i			0.303582i
$807$	−16.8547	−	8.86991i	−0.593312	−	0.312236i
$808$	1.11593	−	4.16469i	0.0392581	−	0.146513i
$809$	22.9981	+	39.8339i	0.808571	+	1.40049i	0.913854	+	0.406044i	$0.133092\pi$
$809$	22.9981	+	39.8339i	0.808571	+	1.40049i	−0.105283	+	0.994442i	$0.533575\pi$
$810$	−8.06241	+	18.4390i	−0.283284	+	0.647881i
$811$	−45.3779			−1.59343			−0.796717	−	0.604352i	$-0.793432\pi$
$811$	−45.3779			−1.59343			−0.796717	+	0.604352i	$0.793432\pi$
$812$	0.858491	+	6.24886i	0.0301271	+	0.219292i
$813$	−1.30137	−	33.2107i	−0.0456411	−	1.16475i
$814$	7.04176	+	4.06556i	0.246813	+	0.142498i
$815$	5.18461	+	9.99924i	0.181609	+	0.350258i
$816$	−1.60012	−	0.362247i	−0.0560155	−	0.0126812i
$817$	−10.7636	−	40.1704i	−0.376572	−	1.40539i
$818$	24.1899	−	24.1899i	0.845781	−	0.845781i
$819$	−1.24729	+	26.5524i	−0.0435837	+	0.927817i
$820$	−6.85980	+	6.26535i	−0.239555	+	0.218795i
$821$	−33.3434	−	19.2508i	−1.16369	−	0.671859i	−0.211508	−	0.977376i	$-0.567837\pi$
$821$	−33.3434	−	19.2508i	−1.16369	−	0.671859i	−0.952187	+	0.305517i	$0.901171\pi$
$822$	7.51231	+	11.9091i	0.262022	+	0.415376i
$823$	0.785245	−	2.93058i	0.0273719	−	0.102153i	−0.950888	−	0.309534i	$-0.899827\pi$
$823$	0.785245	−	2.93058i	0.0273719	−	0.102153i	0.978260	+	0.207380i	$0.0664937\pi$
$824$	6.68365	−	11.5764i	0.232836	−	0.403284i
$825$	2.65259	−	51.6058i	0.0923515	−	1.79668i
$826$	−9.88214	+	4.15864i	−0.343844	+	0.144698i
$827$	−30.2271	−	30.2271i	−1.05110	−	1.05110i	−0.998622	−	0.0524756i	$-0.983289\pi$
$827$	−30.2271	−	30.2271i	−1.05110	−	1.05110i	−0.0524756	−	0.998622i	$-0.516711\pi$
$828$	−0.610390	+	0.216007i	−0.0212125	+	0.00750676i
$829$	−46.3527	+	26.7617i	−1.60990	+	0.929473i	−0.620503	+	0.784204i	$0.713072\pi$
$829$	−46.3527	+	26.7617i	−1.60990	+	0.929473i	−0.989392	+	0.145270i	$0.953595\pi$
$830$	−23.6457	−	7.49779i	−0.820755	−	0.260252i
$831$	2.84590	−	0.883350i	0.0987233	−	0.0306431i
$832$	2.36809	−	2.36809i	0.0820987	−	0.0820987i
$833$	−5.70446	+	3.37967i	−0.197648	+	0.117099i
$834$	−13.8930	−	12.8452i	−0.481074	−	0.444793i
$835$	23.3107	−	36.4594i	0.806700	−	1.26173i
$836$	−25.2389	+	14.5717i	−0.872906	+	0.503973i
$837$	10.7173	−	7.99773i	0.370443	−	0.276442i
$838$	−17.5706	+	4.70802i	−0.606965	+	0.162636i
$839$	−9.47997			−0.327285			−0.163643	−	0.986520i	$-0.552324\pi$
$839$	−9.47997			−0.327285			−0.163643	+	0.986520i	$0.552324\pi$
$840$	3.92575	−	9.46512i	0.135451	−	0.326578i
$841$	−23.3164			−0.804013
$842$	−1.94468	+	0.521075i	−0.0670181	+	0.0179574i
$843$	−16.3870	−	25.9779i	−0.564399	−	0.894726i
$844$	−5.58813	+	3.22631i	−0.192351	+	0.111054i
$845$	−3.89669	+	0.857226i	−0.134050	+	0.0294895i
$846$	0.879455	+	11.2045i	0.0302363	+	0.385219i
$847$	39.9157	+	51.4173i	1.37152	+	1.76672i
$848$	−4.38097	+	4.38097i	−0.150443	+	0.150443i
$849$	−8.54669	−	27.5350i	−0.293322	−	0.944999i
$850$	1.98756	+	4.29881i	0.0681727	+	0.147448i
$851$	−0.254711	+	0.147058i	−0.00873139	+	0.00504107i
$852$	16.4828	+	8.67422i	0.564691	+	0.297174i
$853$	22.4380	+	22.4380i	0.768262	+	0.768262i	0.977800	−	0.209539i	$-0.0671962\pi$
$853$	22.4380	+	22.4380i	0.768262	+	0.768262i	−0.209539	+	0.977800i	$0.567196\pi$
$854$	−28.2491	−	21.4247i	−0.966664	−	0.733139i
$855$	−23.9215	−	22.3894i	−0.818097	−	0.765702i
$856$	−7.86826	+	13.6282i	−0.268931	+	0.465803i
$857$	−11.2662	+	42.0461i	−0.384846	+	1.43627i	0.453562	+	0.891225i	$0.350153\pi$
$857$	−11.2662	+	42.0461i	−0.384846	+	1.43627i	−0.838409	+	0.545042i	$0.816514\pi$
$858$	−29.2734	+	18.4659i	−0.999377	+	0.630414i
$859$	−30.1458	−	17.4047i	−1.02856	−	0.593841i	−0.111990	−	0.993709i	$-0.535723\pi$
$859$	−30.1458	−	17.4047i	−1.02856	−	0.593841i	−0.916573	+	0.399868i	$0.869056\pi$
$860$	−0.861430	+	19.0197i	−0.0293745	+	0.648566i
$861$	18.7465	−	3.32797i	0.638880	−	0.113417i
$862$	−28.8843	+	28.8843i	−0.983804	+	0.983804i
$863$	−4.47160	−	16.6883i	−0.152215	−	0.568075i	−0.999328	−	0.0366613i	$-0.988328\pi$
$863$	−4.47160	−	16.6883i	−0.152215	−	0.568075i	0.847113	−	0.531413i	$-0.178339\pi$
$864$	−5.14215	−	0.747224i	−0.174939	−	0.0254211i
$865$	−28.2036	+	14.6236i	−0.958951	+	0.497217i
$866$	8.66531	+	5.00292i	0.294459	+	0.170006i
$867$	27.8695	−	1.09207i	0.946497	−	0.0370888i
$868$	−5.37848	+	4.17536i	−0.182557	+	0.141721i
$869$	−6.02184			−0.204277
$870$	−7.96800	−	4.66531i	−0.270141	−	0.158169i
$871$	−16.0928	−	27.8736i	−0.545284	−	0.944460i
$872$	2.73857	−	10.2205i	0.0927397	−	0.346109i
$873$	−4.85037	−	13.7061i	−0.164160	−	0.463883i
$874$		−	1.05416i		−	0.0356575i
$875$	−28.5667	+	7.67731i	−0.965732	+	0.259541i
$876$	−16.8701	−	15.5978i	−0.569988	−	0.527002i
$877$	−2.05735	−	7.67812i	−0.0694717	−	0.259272i	0.922451	−	0.386113i	$-0.126183\pi$
$877$	−2.05735	−	7.67812i	−0.0694717	−	0.259272i	−0.991923	+	0.126842i	$0.959516\pi$
$878$	−17.5331	−	4.69797i	−0.591712	−	0.158549i
$879$	−3.10273	+	13.7054i	−0.104652	+	0.462272i
$880$	13.0306	−	2.86657i	0.439260	−	0.0966319i
$881$			5.56368i			0.187445i	0.995598	+	0.0937226i	$0.0298767\pi$
$881$			5.56368i			0.187445i	−0.995598	+	0.0937226i	$0.970123\pi$
$882$	−17.1742	+	12.0850i	−0.578284	+	0.406924i
$883$	4.84514	+	4.84514i	0.163052	+	0.163052i	0.783917	−	0.620865i	$-0.213219\pi$
$883$	4.84514	+	4.84514i	0.163052	+	0.163052i	−0.620865	+	0.783917i	$0.713219\pi$
$884$	1.58609	−	2.74719i	0.0533461	−	0.0923981i
$885$	4.15441	−	15.1349i	0.139649	−	0.508753i
$886$	4.15831	+	7.20240i	0.139701	+	0.241969i
$887$	−2.94804	+	0.789926i	−0.0989856	+	0.0265231i	−0.307972	−	0.951395i	$-0.599650\pi$
$887$	−2.94804	+	0.789926i	−0.0989856	+	0.0265231i	0.208986	+	0.977919i	$0.432984\pi$
$888$	−2.35851	+	0.0924189i	−0.0791463	+	0.00310137i
$889$	16.0826	+	38.2169i	0.539393	+	1.28175i
$890$	−0.843997	−	0.0382259i	−0.0282909	−	0.00128134i
$891$	50.1262	+	19.2657i	1.67929	+	0.645426i
$892$	−8.93499	−	2.39412i	−0.299166	−	0.0801612i
$893$	−17.6746	−	4.73589i	−0.591457	−	0.158480i
$894$	6.01914	+	19.3920i	0.201310	+	0.648564i
$895$	14.2929	−	13.0543i	0.477759	−	0.436358i
$896$	2.62502	+	0.330568i	0.0876957	+	0.0110435i
$897$	−0.0490198	−	1.25097i	−0.00163672	−	0.0417688i
$898$	12.0567	−	3.23058i	0.402336	−	0.107806i
$899$	3.06770	+	5.31341i	0.102313	+	0.177212i
$900$	7.34109	+	13.0808i	0.244703	+	0.436028i
$901$	−2.93428	+	5.08232i	−0.0977549	+	0.169316i
$902$	17.5297	+	17.5297i	0.583676	+	0.583676i
$903$	22.3431	−	31.9882i	0.743531	−	1.06450i
$904$		−	8.31271i		−	0.276476i
$905$	5.62833	+	25.5847i	0.187092	+	0.850465i
$906$	27.8480	+	6.30442i	0.925188	+	0.209450i
$907$	33.6250	+	9.00978i	1.11650	+	0.299165i	0.769466	−	0.638688i	$-0.220523\pi$
$907$	33.6250	+	9.00978i	1.11650	+	0.299165i	0.347033	+	0.937853i	$0.387189\pi$
$908$	2.54238	+	9.48829i	0.0843718	+	0.314880i
$909$	−1.01216	−	12.8952i	−0.0335711	−	0.427705i
$910$	15.2284	+	12.6746i	0.504815	+	0.420159i
$911$		−	13.5125i		−	0.447688i	−0.974625	−	0.223844i	$-0.928139\pi$
$911$		−	13.5125i		−	0.447688i	0.974625	−	0.223844i	$-0.0718605\pi$
$912$	3.93979	−	7.48641i	0.130459	−	0.247900i
$913$	−17.1320	+	63.9375i	−0.566987	+	2.11602i
$914$	15.8181	+	27.3977i	0.523216	+	0.906236i
$915$	50.2127	−	13.1269i	1.65998	−	0.433964i
$916$	9.09422			0.300482
$917$	−9.01605	+	6.99924i	−0.297736	+	0.231135i
$918$	−4.88791	+	0.576966i	−0.161325	+	0.0190427i
$919$	23.3642	+	13.4893i	0.770714	+	0.444972i	0.833129	−	0.553078i	$-0.186547\pi$
$919$	23.3642	+	13.4893i	0.770714	+	0.444972i	−0.0624154	+	0.998050i	$0.519880\pi$
$920$	−0.145871	+	0.460033i	−0.00480923	+	0.0151668i
$921$	0.856726	−	3.78435i	0.0282301	−	0.124698i
$922$	3.42209	+	12.7714i	0.112701	+	0.420604i
$923$	−25.4656	+	25.4656i	−0.838212	+	0.838212i
$924$	−25.7051	−	9.32210i	−0.845636	−	0.306675i
$925$	4.36272	+	5.23379i	0.143445	+	0.172086i
$926$	−19.8816	−	11.4786i	−0.653349	−	0.377211i
$927$	7.31625	−	39.4289i	0.240297	−	1.29501i
$928$	0.617033	−	2.30280i	0.0202551	−	0.0755931i
$929$	24.7230	−	42.8215i	0.811135	−	1.40493i	−0.100936	−	0.994893i	$-0.532184\pi$
$929$	24.7230	−	42.8215i	0.811135	−	1.40493i	0.912071	−	0.410033i	$-0.134483\pi$
$930$	0.0607534	−	9.96708i	0.00199218	−	0.326833i
$931$	−9.22023	−	32.9232i	−0.302181	−	1.07901i
$932$	13.2264	+	13.2264i	0.433244	+	0.433244i
$933$	4.84776	−	9.21173i	0.158708	−	0.301578i
$934$	11.3029	−	6.52572i	0.369841	−	0.213528i
$935$	11.2193	−	5.81724i	0.366912	−	0.190244i
$936$	4.32722	−	9.06732i	0.141440	−	0.296375i
$937$	−11.4941	+	11.4941i	−0.375495	+	0.375495i	−0.869474	−	0.493979i	$-0.835542\pi$
$937$	−11.4941	+	11.4941i	−0.375495	+	0.375495i	0.493979	+	0.869474i	$0.335542\pi$
$938$	9.59817	−	23.5461i	0.313391	−	0.768806i
$939$	−3.77967	+	4.08796i	−0.123345	+	0.133406i
$940$	7.05779	+	4.51247i	0.230200	+	0.147181i
$941$	29.1043	−	16.8034i	0.948774	−	0.547775i	0.0560744	−	0.998427i	$-0.482142\pi$
$941$	29.1043	−	16.8034i	0.948774	−	0.547775i	0.892700	+	0.450651i	$0.148808\pi$
$942$	3.68629	−	2.32534i	0.120106	−	0.0757636i
$943$	−0.866165	+	0.232088i	−0.0282062	+	0.00755783i
$944$	4.05235			0.131893
$945$	1.62959	−	30.6976i	0.0530104	−	0.998594i
$946$	50.8047			1.65180
$947$	−48.9361	+	13.1124i	−1.59021	+	0.426095i	−0.942067	−	0.335424i	$-0.891120\pi$
$947$	−48.9361	+	13.1124i	−1.59021	+	0.426095i	−0.648142	+	0.761520i	$0.724454\pi$
$948$	1.47846	−	0.932621i	0.0480180	−	0.0302901i
$949$	38.4729	−	22.2124i	1.24888	−	0.721044i
$950$	−24.0640	+	4.16242i	−0.780739	+	0.135047i
$951$	−0.925217	+	1.00068i	−0.0300022	+	0.0324494i
$952$	2.48276	−	0.341090i	0.0804667	−	0.0110548i
$953$	−26.3451	+	26.3451i	−0.853401	+	0.853401i	−0.990550	−	0.137149i	$-0.956206\pi$
$953$	−26.3451	+	26.3451i	−0.853401	+	0.853401i	0.137149	+	0.990550i	$0.456206\pi$
$954$	−8.00537	+	16.7746i	−0.259183	+	0.543097i
$955$	17.6935	−	55.7998i	0.572548	−	1.80564i
$956$	7.68765	−	4.43847i	0.248636	−	0.143550i
$957$	−11.4743	+	21.8035i	−0.370912	+	0.704808i
$958$	22.2217	+	22.2217i	0.717951	+	0.717951i
$959$	−17.1371	−	12.9972i	−0.553387	−	0.419700i
$960$	−2.75525	+	2.72187i	−0.0889255	+	0.0878480i
$961$	12.1885	−	21.1110i	0.393176	−	0.681001i
$962$	1.18119	−	4.40825i	0.0380830	−	0.142128i
$963$	−8.61297	+	46.4172i	−0.277549	+	1.49577i
$964$	3.57384	+	2.06335i	0.115105	+	0.0664562i
$965$	47.5414	+	2.15322i	1.53041	+	0.0693147i
$966$	0.756916	−	0.636627i	0.0243534	−	0.0204831i
$967$	−38.9797	+	38.9797i	−1.25350	+	1.25350i	−0.299362	+	0.954139i	$0.596774\pi$
$967$	−38.9797	+	38.9797i	−1.25350	+	1.25350i	−0.954139	+	0.299362i	$0.903226\pi$
$968$	−6.36761	−	23.7642i	−0.204663	−	0.763812i
$969$	1.76931	−	7.81543i	0.0568384	−	0.251068i
$970$	−10.3299	−	3.27550i	−0.331673	−	0.105170i
$971$	8.61828	+	4.97576i	0.276574	+	0.159680i	0.631871	−	0.775073i	$-0.282287\pi$
$971$	8.61828	+	4.97576i	0.276574	+	0.159680i	−0.355298	+	0.934753i	$0.615620\pi$
$972$	−15.2905	+	3.03316i	−0.490444	+	0.0972886i
$973$	26.7644	+	10.9101i	0.858028	+	0.349761i
$974$	−26.6188			−0.852921
$975$	−28.3632	+	6.05855i	−0.908349	+	0.194029i
$976$	6.70029	+	11.6052i	0.214471	+	0.371475i
$977$	6.54016	−	24.4082i	0.209238	−	0.780888i	−0.778877	−	0.627176i	$-0.784211\pi$
$977$	6.54016	−	24.4082i	0.209238	−	0.780888i	0.988116	−	0.153712i	$-0.0491228\pi$
$978$	−4.06312	+	7.72076i	−0.129924	+	0.246883i
$979$			2.25446i			0.0720527i
$980$	−0.532117	+	15.6434i	−0.0169978	+	0.499711i
$981$	−2.48391	−	31.6457i	−0.0793051	−	1.01037i
$982$	−4.45486	−	16.6258i	−0.142160	−	0.530550i
$983$	22.0513	+	5.90862i	0.703326	+	0.188456i	0.592720	−	0.805409i	$-0.298054\pi$
$983$	22.0513	+	5.90862i	0.703326	+	0.188456i	0.110606	+	0.993864i	$0.464721\pi$
$984$	−7.01870	−	1.58894i	−0.223748	−	0.0506536i
$985$	−14.3030	+	22.3707i	−0.455730	+	0.712791i
$986$		−	2.25818i		−	0.0719151i
$987$	−7.27350	−	15.5509i	−0.231518	−	0.494990i
$988$	11.5664	+	11.5664i	0.367975	+	0.367975i
$989$	−0.918842	+	1.59148i	−0.0292175	+	0.0506061i
$990$	33.9832	−	21.1484i	1.08006	−	0.672140i
$991$	−19.6593	−	34.0510i	−0.624500	−	1.08166i	−0.988637	−	0.150320i	$-0.951970\pi$
$991$	−19.6593	−	34.0510i	−0.624500	−	1.08166i	0.364138	−	0.931345i	$-0.381364\pi$
$992$	2.48585	−	0.666080i	0.0789257	−	0.0211481i
$993$	1.46333	+	37.3438i	0.0464373	+	1.18507i
$994$	−28.2286	−	3.55482i	−0.895357	−	0.112752i
$995$	28.8148	+	31.5488i	0.913491	+	1.00016i
$996$	−5.69602	−	18.3509i	−0.180485	−	0.581472i
$997$	−11.1081	−	2.97640i	−0.351797	−	0.0942636i	0.0785932	−	0.996907i	$-0.474957\pi$
$997$	−11.1081	−	2.97640i	−0.351797	−	0.0942636i	−0.430390	+	0.902643i	$0.641624\pi$
$998$	−39.0211	−	10.4557i	−1.23519	−	0.330969i
$999$	−6.57768	+	2.62184i	−0.208109	+	0.0829512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.23.15	yes	64
3.2	odd	2	inner	210.2.x.a.23.3	✓	64
5.2	odd	4	inner	210.2.x.a.107.11	yes	64
7.4	even	3	inner	210.2.x.a.53.2	yes	64
15.2	even	4	inner	210.2.x.a.107.2	yes	64
21.11	odd	6	inner	210.2.x.a.53.11	yes	64
35.32	odd	12	inner	210.2.x.a.137.3	yes	64
105.32	even	12	inner	210.2.x.a.137.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.3	✓	64	3.2	odd	2	inner
210.2.x.a.23.15	yes	64	1.1	even	1	trivial
210.2.x.a.53.2	yes	64	7.4	even	3	inner
210.2.x.a.53.11	yes	64	21.11	odd	6	inner
210.2.x.a.107.2	yes	64	15.2	even	4	inner
210.2.x.a.107.11	yes	64	5.2	odd	4	inner
210.2.x.a.137.3	yes	64	35.32	odd	12	inner
210.2.x.a.137.15	yes	64	105.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.46494 - 0.924094i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.480420 - 2.18385i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.29210 - 2.70749i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.46494 - 0.924094i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.480420 - 2.18385i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.29210 - 2.70749i) q^{9} +(-1.02927 - 1.98509i) q^{10} +(-5.16739 + 2.98339i) q^{11} +(0.806628 - 1.53276i) q^{12} +(2.36809 + 2.36809i) q^{13} +(-0.330568 + 2.62502i) q^{14} +(-2.72187 - 2.75525i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.245156 - 0.914934i) q^{17} +(0.547324 - 2.94965i) q^{18} +(4.22990 + 2.44213i) q^{19} +(-1.50798 - 1.65106i) q^{20} +(0.800996 + 4.51203i) q^{21} +(-4.21916 + 4.21916i) q^{22} +(-0.0558604 - 0.208474i) q^{23} +(0.382436 - 1.68930i) q^{24} +(-4.53839 + 2.09833i) q^{25} +(2.90030 + 1.67449i) q^{26} +(-0.609122 - 5.16033i) q^{27} +(0.360100 + 2.62113i) q^{28} +2.38403 q^{29} +(-3.34224 - 1.95690i) q^{30} +(1.28677 + 2.22875i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.81298 + 9.14565i) q^{33} -0.947209i q^{34} +(5.83027 + 1.00399i) q^{35} +(-0.234751 - 2.99080i) q^{36} +(-0.352701 - 1.31630i) q^{37} +(4.71784 + 1.26414i) q^{38} +(5.65744 + 1.28077i) q^{39} +(-1.88392 - 1.20451i) q^{40} -4.15479i q^{41} +(1.94150 + 4.15097i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(-2.98339 + 5.16739i) q^{44} +(-6.53349 - 1.52102i) q^{45} +(-0.107914 - 0.186912i) q^{46} +(-3.61867 + 0.969620i) q^{47} +(-0.0678189 - 1.73072i) q^{48} +(-5.00516 - 4.89371i) q^{49} +(-3.84066 + 3.20145i) q^{50} +(-0.486346 - 1.56687i) q^{51} +(3.23487 + 0.866780i) q^{52} +(-5.98451 - 1.60355i) q^{53} +(-1.92396 - 4.82684i) q^{54} +(8.99780 + 9.85151i) q^{55} +(1.02623 + 2.43862i) q^{56} +(8.45331 - 0.331246i) q^{57} +(2.30280 - 0.617033i) q^{58} +(2.02618 + 3.50944i) q^{59} +(-3.73484 - 1.02519i) q^{60} +(-6.70029 + 11.6052i) q^{61} +(1.81977 + 1.81977i) q^{62} +(5.34295 + 5.86966i) q^{63} -1.00000i q^{64} +(4.03387 - 6.30922i) q^{65} +(-2.28191 + 10.0797i) q^{66} +(-9.28310 - 2.48740i) q^{67} +(-0.245156 - 0.914934i) q^{68} +(-0.274482 - 0.253781i) q^{69} +(5.89146 - 0.539201i) q^{70} +10.7537i q^{71} +(-1.00083 - 2.82813i) q^{72} +(3.43327 - 12.8131i) q^{73} +(-0.681365 - 1.18016i) q^{74} +(-4.70942 + 7.26783i) q^{75} +4.88427 q^{76} +(-2.14864 - 15.6397i) q^{77} +(5.79616 - 0.227124i) q^{78} +(0.874016 + 0.504613i) q^{79} +(-2.13148 - 0.675868i) q^{80} +(-5.66096 - 6.99668i) q^{81} +(-1.07534 - 4.01322i) q^{82} +(7.84434 - 7.84434i) q^{83} +(2.94970 + 3.50703i) q^{84} +(-2.11586 - 0.0958303i) q^{85} +(-7.37384 - 4.25729i) q^{86} +(3.49247 - 2.20307i) q^{87} +(-1.54432 + 5.76347i) q^{88} +(0.188917 - 0.327214i) q^{89} +(-6.70454 + 0.221800i) q^{90} +(-8.16688 + 3.43682i) q^{91} +(-0.152613 - 0.152613i) q^{92} +(3.94461 + 2.07589i) q^{93} +(-3.24441 + 1.87316i) q^{94} +(3.30112 - 10.4107i) q^{95} +(-0.513452 - 1.65420i) q^{96} +(3.42689 - 3.42689i) q^{97} +(-6.10120 - 3.43153i) q^{98} +(1.40071 + 17.8455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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